Hedonic Quality Adjustment Methods For Microwave Ovens In the U.S. CP

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Hedonic Quality Adjustment Methods For Microwave Ovens In the U.S. CPI

Paul R. Liegey1PrefaceThe U.S. Consumer Price Index (CPI) for Major Appliances would have increased

0.6 percent instead of the official index increase of 0.8 percent if hedonic quality

adjustment methods had been applied to microwave oven (substitution) price changes from

August 1999 through April 2000 (see attachment 1). This quality adjusted empirical result

provides a more refined measure of price inflation for Major Appliances since there

are a greater number of “pure” price changes used to calculate this item

stratums’ price index. Of the three different approaches or methods that use the results from hedonic

regression models to quality adjust price indexes, BLS employs the ‘matched model’ method

in its official indexes.2 This method controls for quality changes based on the

difference in product specifications or characteristics between two items when a

substitute observation, or quote, occurs in the price index sample. It is important to

note that under the ‘matched model’ approach only substitution price changes, or

quotes, are eligible for hedonic quality adjustments. As previously announced, the Bureau of Labor Statistics (BLS) is extending the use of

quality adjustments derived from hedonic models in the CPI. A hedonic model decomposes the

price of a consumer product into implicit prices for each of its important features

and components, thereby providing an estimate of the value for each price influencing

feature and component. Effective with the CPI for July 2000, BLS has extended hedonic quality adjustments to

Microwave ovens and Refrigerators, two products in the Major Appliances item

stratum. The relative importance (share of weight), as of December 1999, for this stratum

was 0.205 percent in the CPI for all Urban Consumers (CPI-U) and 0.236 percent in the CPI

for Urban Wage Earners and Clerical Workers (CPI- W). Within Major Appliances,

Microwave ovens are estimated to represent 11 percent of the weight and Refrigerators

about 33 percent. In October 2000, BLS will further extend hedonic quality adjustments to

Washers and Dryers, two other products in the Major Appliances item stratum. The

remaining products in this stratum—those that will not be subject to hedonic quality

adjustment at this time—include Freezers and Stoves and Ovens.BackgroundIn 1947, Raytheon demonstrated the world’s first microwave oven and called it a

“Radarange.”3 The first microwave ovens cost between two and three

thousand dollars and were sold primarily to the commercial marketplace. By the early

1950s, U.S. appliance makers began showing interest in the microwave oven since it had the

ability to provide more flexibility to the consumer by reducing the time needed to cook

different meals. In 1955, the Tappan Stove Company—under a licensing agreement with

Raytheon—brought the first consumer microwave ovens to the U.S. market with a price tag

of $1,300. These first consumer microwave ovens were more compact and less powerful than

their “Radarange” predecessors and reflected only modest sales at their price

range.In 1965, Raytheon acquired Amana Refrigerators, Incorporated—an appliance maker with a

well established distribution channel—and, in 1967, introduced to the U.S. market the

first “countertop” model of microwave ovens that sold for $495 retail and were

smaller, safer and more reliable than previous models. By 1986, 25 percent of U.S.

households owned a microwave oven, up from less than one percent in 1971.4 Assuming

microwave oven penetration into U.S. households was constant during this 15 year period,

about 12 to 13 percent of U.S. households would have owned a microwave oven in 1978.The microwave oven was introduced into the CPI sample in 1978.5 Since its’

inception to the CPI, microwave ovens have been represented in three item stratum price

indexes over three CPI revisions:

With the release of the revised CPI in January 1978, microwave ovens became part of the Stoves,

dishwashers, vacuums, and sewing machines item stratum price index. The index level

for this item stratum in December 1977 was 100.0 (its base year), and increased to 117.4

by December 1986 — an overall price index increase of 17.4 percent for the 9 year period.

With the release of the revised CPI in January 1987, microwave ovens became part of the Stoves,

ovens, dishwashers, and air conditioners item stratum price index. The index level for

this item stratum in December 1986 was 100.0 (its base year), and decreased to 91.6 by

December 1997 — an overall price index decline of 8.4 percent for the 11 year period. Finally, with the release of the revised CPI in January 1998, microwave ovens became

part of the Major Appliances item stratum price index. The index level for this

item stratum in December 1997 was 100.0 (its base year), and through March 2000 is 97.9 —

an overall price index decline of 2.1 percent for the most recent two and a quarter year

period. Today, more than 90 percent of U.S. households own a microwave oven.6 As

consumer expenditures on microwave ovens have increased through time in the U.S. economy,

so too have their representation in the CPI — currently accounting for 11 percent of the

weight in the Major Appliances item stratum price index. Microwave ovens were selected as a product that would benefit from hedonic regression

modeling since manufacturers provide a vast range of sizes, configurations, and features.

In the Consumer Digest’s 2000 Annual Buying Guide, the latest annual review on

microwave ovens notes that

“today’s ovens are safer, more convenient and offer a wealth of advanced features.

Current models produce about 10 percent more power than previous versions and many include

electronic sensors along with automatic controls for easy programming of cooking commands.

They also come in a greater variety of sizes. From tiny no-frills models to sophisticated

ovens large enough to handle full-size meals, microwave ovens are ready to meet a broad

range of (consumer) needs. The best part is that some of these advanced features are now

available at lower prices.”7These newer models of microwave ovens are included for price index calculations only if

older models being used in the price index sample are no longer available (in the CPI

outlets) for CPI pricing. When a newer model replaces an older model in the CPI, the price

change that is used in the index is referred to as substitution price change. Substitution

price change can be either “pure” (directly compared or quality adjusted) or

“imputed” (non-comparable). From August 1999 through April 2000 Major Appliances employed, on average, 215

price changes to calculate its U.S. level monthly price index (see attachment 2).

Approximately 10 percent, or 22, of these price changes were substitution price changes.

In comparison, microwave ovens accounted for, on average, 39 of the 215 price changes used

to calculate Major Appliances index, and averaged (just) four substitutions per

month from August 1999 through April 2000. DataSample selection for the Hedonic ModelThe official CPI sample of microwave oven prices used to calculate the Major

Appliances CPI was too small for hedonic regression estimation. Using a process that

mimics the official CPI sample selection process, an additional sample of 195 consumer

businesses, or outlets, was chosen to augment the official CPI sample for microwave ovens.

This additional outlet sample was used to select a sample of microwave oven prices. The

supplementary sample was used only for estimating the hedonic regression model for

microwave ovens.8CPI field economists were instructed to collect a total of 390 microwave oven prices in

the sample of 195 additional outlets. Individual microwave oven brand and models were

selected by grouping all microwave ovens in a particular outlet into two groups—the

“standard” microwave ovens and “better model” or higher quality

microwave ovens. Once categorized into these two groups, the CPI field economist was

instructed to select a “good selling” microwave oven from each of the

“standard” and “better model” groups. About 73 percent of the additional sample price quotes that were collected for

microwave ovens had price and characteristic data that could be used in the regression

model. The most common reason that CPI field economists could not collect the additional

sample price quotes for microwave ovens was respondent refusal.9 A total of 381

prices—and characteristic descriptions—were used to estimate the hedonic model for

microwave ovens. This total sample consists of 98 official CPI observations and 283

additional sample observations.Price and Characteristic Data for the Hedonic ModelAll of the price and characteristic data used for the microwave oven hedonic model was

captured on CPI data collection documents, or checklists, for this item (see last

attachment). The prices that were collected for the microwave oven sample represent “retail

offer” prices. As the name suggests, a retail offer price represents what a consumer

business is willing to sell an item for which may, or may not, differ from the transaction

price—what a consumer actually paid for the item. Retail offer prices, like transaction

prices, may change through time depending on whether the item being sold is offered at a

“regular” price or a “sale” price. The set of quality attributes collected for each of the 381 microwave ovens in the

sample are represented on the CPI checklist for this item (see last attachment). In each

of the quality characteristic categories, CPI field economists selected the specific

characteristic element that best described the item they were pricing. For example, if an

Amana countertop model with a (oven) capacity of 1.6 cubic feet and cooking power of 1000

watts had been selected by the field economist, this would be designated on the CPI data

collection document by selecting the A1, B1, D3, and E2 specification elements—see last

attachment. When possible, secondary source information such as manufacturer websites and consumer

information magazines—including Consumer Digest’s and Consumer Reports—were

used to verify the accuracy of the characteristic data collected on the CPI checklist for

microwave ovens. Overall, the CPI field economists were able to provide complete,

consistent, and accurate descriptions for most microwave oven observations included in the

hedonic regression sample. ModelThe hedonic model that was specified for microwave ovens in this study resembles the

categories of quality characteristics that are presented on the CPI checklist for this

item (see last attachment):ln P = b0 + b1 Type + b2 Capacity + b3 Brand

+ b4 Oven

Controls + b5 Features + b6 Control + e.The bi’s in

this model represent the effect of the characteristics on the natural logarithm of price.

The CPI prices that were collected in this sample represent “retail offer”

prices, and approximately 37 percent of these prices were collected “on sale.”

The mean price for all microwave ovens in the sample was $207.75. The mean price for

“regular” priced microwave ovens in the sample is $214.77 and the mean price for

“sale” priced microwave ovens is $195.61. Since type of price (that is, regular

or sale) is thought to have an impact on the overall price level, a dummy variable for

sale price was included in the model to capture this effect, and its expected coefficient

sign was negative. A priori expectations about which microwave oven characteristics influence price

were developed, when possible, on industry information, manufacturer websites, and

consumer information magazines.

Microwave Oven TypesBasically, two types of microwave ovens are sold in today’s appliance market. Countertop

models are more frequently advertised by manufacturers and retailers and accounted for

approximately 76 percent of the microwave ovens in the sample. Consumers who have smaller

kitchens and lack counter space can opt for an over-the-range model—this

type of microwave oven accounted for the remaining 24 percent of the microwave oven

sample. All over-the-range models come with an installation kit for

mounting. In addition, since over-the-range models take the place of a

range or stove exhaust hood, all come with a ventilation fan that exhaust both the range

and microwave oven cooking gases. The mean prices for the 288 countertop

models and 93 over-the-range models in the hedonic sample were $140.64

and $416.31, respectively. By way of comparison, a December 1999 Consumer Reports

study on microwave ovens found that the countertop ovens they tested sold

for $200 or less while over-the-range models typically sold for about

$350 to $450.10 Dummy or indicator variables were created for both types of

microwave ovens. The over-the-range variable was included in preliminary

models and was expected to have a large, positive impact on price. Both the size and cooking power characteristics of microwave ovens are also assumed to

have a significant impact on microwave oven prices. Manufacturers and retailers advertise

size in terms of cubic feet and cooking power in terms of maximum watts. Both size and

cooking power assume a wide range of numeric values—see the CPI checklist for microwave

ovens (last attachment). To accommodate this wide range of values, continuous variables

were created for both cavity cubic feet and maximum watt cooking.

It was assumed that the price of the microwave oven would increase with increasing values

for one or both of these variables. For example, a 2.0 cubic foot oven with 1100 watts of

cooking power is assumed to sell for a higher price than a 0.8 cubic foot oven with 700

watts of cooking power ceteris paribus. A preliminary model was specified with two dummy variables, sale price

and above stove, and two continuous variables, cavity cubic feet

and maximum wattage (see attachment 3, Iterative regression 1). This

model specification proved to explain a significant portion of the variation in (the

natural log of) price with an R2 of slightly more than 82 percent. While the

magnitude, direction and significance of the parameter estimates in the preliminary model

generally conformed with a priori expectations, somewhat low tolerance values for

the cavity cubic feet and maximum wattage variables

indicated that multicollinearity might be present in the model. Further investigation

revealed that the pearson correlation coefficient, or measure of collinearity, for these

two variables was positive and strong at 0.61—they tend to move together and can serve as

a proxy for each other. The existence of multicollinearity causes the standard errors of

the correlated variables to increase and the associated parameter estimates to be

imprecise.11 Subsequent variations of this preliminary model—not included in

Attachment 3—revealed that the variable for cavity cubic feet provided a

better overall fit for the model and was included in the final model.Microwave Oven BrandsBrand was the next category of quality characteristics used to specify the

hedonic model for microwave ovens. In addition to the 9 brands listed on the CPI checklist

for this item (see last attachment), dummy or indicator variables were created for 7

additional brands that were collected in the “Other brand” specification

element—see B99 specification element on the CPI checklist. Separate variables were

created for each brand rather than trying to categorize them into “high

quality,” “medium quality,” and “low quality” groups since little

secondary source information was available about ranking quality of microwave ovens by

brand.

Asan established leader in the production and distribution of

microwave ovens, Amana was thought to have a positive impact on price.

Inclusion of the brand variables with the previous model specification—see attachment 3,

Iterative regression 2—yielded a slightly better fit with an R2 of 87 percent.

In the absence of strong a priori about brands, low tolerance values and

statistically insignificant parameter estimates led to the exclusion of some of the brand

name variables. Subsequent variations of this preliminary model—not included in

Attachment 3—and inclusion of other quality category variables on the CPI checklist led

to the following brands being included in the final model: Amana, Kitchenaid,

General Electric, Whirlpool, Samsung, Admiral,

Emerson, and Sanyo. Interestingly enough, the recent report on the CPI by The Conference Board, notes that

“In existing products, probably the biggest problem in quality change that the CPI

never recognizes (is) the subtle, often gradual changes that are difficult to detect and

to measure. These would include for example,

reduced incidence of repairs to

household appliances

“12 Coincidentally, a December 1999 Consumer

Reports study on microwave ovens supplies data about percent of “repairs and

serious problems” for microwave oven brands (see Attachment 4). This data was

compared to the implicit price values estimated in the final hedonic regression model for

microwave ovens to see if consumer valuation of brand was consistent across studies. Of

the eight brands included in the final hedonic model and the 12 brands included in the Consumer

Reports study, six brands were common to both studies. The following is an ordinal

ranking of brand value for both studies results Consumer Reports Percent of Repairs BrandsHedonic Brand Variables Ranking  Ranking1SamsungAmanaA2SanyoGeneral ElectricB3EmersonWhirlpoolC4General ElectricSamsungD5WhirlpoolEmersonE6AmanaSanyoF 1 = least repairs 6 = most repairs A = most positive contribution to price F = most negative contribution to priceA cursory comparison of the two studies reveals that brands in the hedonic model with

the most positive implicit price values have more “repairs and serious

problems” while brands with the most negative implicit price values have less

“repairs and serious problems.” This (limited) comparison of brand quality seems

to suggest that repair histories do not (in and of themselves) influence relative price

levels for microwave oven brands.Microwave Oven ControlsOven Control characteristics in the “Type of Controls,” “Number

of Power Settings,” and “Number of Pre-Set Programming Stages”

specification categories on the CPI checklist (see last attachment) were next considered

in specifying the hedonic regression model for microwave ovens.

In the “Type of Controls” specification category, dummy variables were

created for electronic controls and manual controls.

While most of the microwave ovens in today’s appliance market possess touch sensitive or electronic

controls, some manufacturers still offer models with push button or rotary dial manual

controls. Almost 95 percent of the microwave oven sample contained microwave

ovens with electronic controls, but a variable for manual

controls was included in a preliminary model—see attachment 3, iterative

regression 3—since a priori expectations were that only inferior quality models

possessed this type of control. As expected, the parameter estimate for the manual

controls variable was negative, remained robust in subsequent regressions, and

was included in the final model.Most microwave ovens can control the (total) cooking power or wattage—most commonly

this feature is given in 10 percent increments ranging from a low power of 10 percent to a

high power of 100 percent. The December 1999 Consumer Reports study on microwave

ovens notes that “most models” have 10 power settings.13

Similarly, most of the observations in the microwave oven sample were described as

possessing 10 power settings. Other values collected for this

specification element were “manual setting,” “not specified,” and

“not applicable.” Since 10 power settings was the only

specification element listed in the “Number of Power Settings” category and no

other meaningful variables could be created, the 10 power settings

variable was not included in the final model.A less advertised characteristic on microwave ovens is the “Number of Pre-Set

Programming Stages.” This oven control allows the user to pre-set or pre-program the

microwave oven to cook food at a certain power setting for a certain length of time and

then automatically switch to a different power setting for another length of time. An

example of this feature might be programming the microwave oven to cook a food for two

minutes at defrost, three minutes at a high temperature and one-minute at a low

temperature. It was assumed that microwave ovens with a higher number of sequential cooking stages

offered more convenience and greater value to the consumer than microwave ovens with a

lesser number of sequential cooking stages ceteris paribus. However, the December

1999 Consumer Reports study on microwave ovens notes that “most models can be

programmed to cook for at least two sequential stages and up to about 100 minutes in

all.”14Dummy variables were created similar to the specification elements on the CPI checklist

(see last attachment) for the “Number of Pre-Set Programming Stages.” In

particular, variables for 4 stage, 3 stage, and 2

stage programming were tested in a preliminary model—see attachment 3, iterative

regression 3. While the parameter estimates for 3 stage and 2

stage programming were marginally negative and statistically insignificant, the

parameter estimate for 4 stage programming was positive and statistically

significant. Subsequent variations of this preliminary model—not included in Attachment

3—and inclusion of other quality category variables led to the 4 stage

programming variable remaining in the final model.Microwave Oven FeaturesManufacturers and retailers of microwave ovens offer and advertise a variety of features

on their products. Microwave oven features are represented in the “Cavity

Features,” “Cooking Features,” and “Programming Features”

specification categories on the CPI checklist (see last attachment) for microwave ovens.

Dummy or indicator variables were created for all characteristics in these specification

categories. Each category of variables was tested to see whether the overall fit of the

model could be enhanced. Basic preliminary models used to test each category of features

are presented in Attachment 3, iterative regressions 4 through 6.Of the 19 dummy variables that were created for the three categories of feature

specifications, only four of these variables—built-in sensor, auto

sensor, convection cook, and convection broil—were

used in the final regression model for microwave ovens. In addition, since these

characteristics were not clearly delineated on the CPI checklist—or in the product

descriptions at the retail outlets—the built-in sensor and auto sensor variables were

combined into one variable called sensor and the convection cook and

convection broil variables were combined into one variable called convection.

Sensor technology helps prevent undercooking or overcooking food. Through

measures such as gauging the release of steam as food heats, sensor(s)

detect the degree to which food has cooked and adjusts heating time or cooking power

accordingly. This feature is more common in today’s microwave ovens and was reported in 54

percent of the 381 microwave ovens included in the sample. It was expected a priori

that this feature would have a mild to moderate positive influence on price. Since the

parameter estimate for sensor was positive, statistically significant,

and remained robust in subsequent variations of preliminary models—included and not

included in Attachment 3—the sensor variable remained in the final

model.

Microwave ovens with convection cooking rely on a fan that gently

circulates heated air over and around the food, producing golden brown exteriors and moist

interiors. Convection microwaves ovens can function as normal microwaves

ovens, as a regular convection oven, or a combination of the two at once. This feature was

reported for about five percent of the microwave oven sample and was expected a priori

to have a strong positive influence on price. Since the parameter estimate for convection

was positive, statistically significant, and remained robust in subsequent

variations of preliminary models—included and not included in Attachment 3—the convection

variable remained in the final model.Most other microwave oven feature variables were excluded from the final regression

model because of their poor performance in preliminary and subsequent regression models.

For example, all of the feature parameter estimates in the “Programming

Features” specification category consistently reflected small nominal impacts on

price and were statistically insignificant. These kinds of features are frequently touted

by retailers and manufacturers as value enhancing but typically do not contribute

(substantially) to the price—or value—of microwave ovens that possess them. Microwave Oven Miscellaneous SpecificationsOther CPI checklist specification categories that were examined for hedonic model

development included optional installation kits for countertop models as

well as delivery charges. These CPI categories were found to be, for the

most part, not representative of the microwave oven market. On the few occasions that

either the cost of optional installation kits or delivery

charges were reported with the price of the microwave oven, these additional charges were

“backed out” of the overall price so that just the price of the microwave oven

was reflected in the sample data.Similarly, the manufacturer warranty specification category on the CPI

checklist could not be utilized in specifying the hedonic model for microwave ovens.

Almost all microwave ovens that are sold in today’s market come with a standard one year

parts and labor manufacturer warranty. Since this was the predominant

type of manufacturer warranty captured in the microwave oven sample, it

could not be used in the final regression model.Finally, the country of origin specification category on the CPI

checklist was tested to see if the hedonic model for microwave ovens could be fitted with

any of these variables. Country of origin represents the country in which

the product—in this case microwave ovens—was constructed and is believed to serve as a

proxy for the quality of a good and service. In the sample used in this study, over 90

percent of the 381 microwave ovens were constructed in six different countries. In

particular, microwave ovens constructed in the USA, Japan, Korea, China, Singapore, and

Thailand accounted for 42, 8, 16, 6, 10, and 9 percent of the sample data, respectively. In the absence of a priori about country of origin, low

tolerance values and statistically insignificant parameter estimates led to the exclusion

of most of the country of origin variables. Only the parameter estimate

for Korea was statistically significant and remained in the final

regression model.Control VariablesVarious control variables were tested representing region of

the country, city size, and type of business as

defined in the CPI. The most consistently performing and statistically significant control

variables that were included in the final microwave oven model were appliance

stores, warehouse outlets, and A size cities

(populations 1,000,000 or greater) in theNortheast and

West regions. The purpose of control variables are to minimize

the unexplained variation that might remain after the model has been fitted with price

determining characteristics.Attachment 3, iterative regressions 1 through 7, are included in this study to give the

reader a sense of how the hedonic model for microwave ovens progressed as more categories

of CPI variables were considered for model inclusion. Iterative regressions—both included

and not included in Attachment 3—were performed until the remaining parameter estimates

in the model below exhibited relative robustness to the inclusion and deletion of other

variables not included. The direction and magnitude of the parameter estimates seem

reasonable, and the statistics pertaining to fit, significance, and collinearity are

within generally accepted limits.Variable CategoryVariable NameParameter EstimateT StatisticTolerance Intercept4.410015108.817 Type of Price:Sale Price-0.077066-4.1220.8536454Oven Type:Above Stove or Range0.93841040.7750.7101415Table

or CountertopBase  Brand:Amana0.4579598.9970.8134151Kitchenaid0.4533395.3870.9442307General Electric0.1850566.5990.7371506Whirlpool0.1308823.0630.8452731Other brands not listedBase  Samsung-0.122763-2.6280.8414810Admiral-0.173660-2.6860.9210839Emerson-0.195389-2.8060.9242426Sanyo-0.228115-2.3700.9594545Oven Cavity Capacity(in cubic feet)Capacity (per cubic foot)0.33629312.7760.7596359Type of Controls:Electronic or Touch SensitiveBase  Manual or Push Button-0.194143-4.7990.8532257Memory Programming:(number

of stages) 4 Stage Programming0.1018374.1670.9007655No Stage Programming Base  Features:Convection Cook/Broil0.3296757.6520.8778186Auto or Built-In Sensor0.0574333.1270.8274627Country of Origin:Other countries not listedBase  Korea-0.069286-2.5340.7001641Type of Outlet:Appliance outlet0.0847154.0720.6637763Warehouse outlet-0.223390-2.6200.9197068Control Variables:A size city/Northeast region 0.0626192.2650.8554760A size city/West region0.0734882.9210.8623244R2=0.9168Adjusted R2=0.9121F value=198.783Number of observations=381Hedonic Quality Adjustments and Price Index SimulationBLS employs the ‘matched model’ method of quality adjustment in its official indexes.

This method controls for quality changes based on the difference in product specifications

or characteristics between two items when a substitute observation, or quote, occurs in

the price index sample. It is important to note that under the ‘matched model’ approach only

substitution price changes, or quotes, are eligible for hedonic quality adjustments.

During the study period from August 1999 through April 2000, a total of 39 microwave

oven substitution price changes—an average of (just) four per month—occurred in the Major

Appliances price index sample. For each microwave oven substitution price quote,

differences in the specification or characteristic data of the old and new items were

identified to see if the parameter estimates in the hedonic model could be utilized to

quality adjust the official price change. Approximately 54 percent, or 21, of the 39 microwave oven substitute price changes in

the study were quality adjusted based on specification differences between substitute

items. The most common type of quality adjustment performed for microwave ovens in this

study was for changes in capacity—represented in more than 80 percent of

the quality adjusted (substitution) prices. Other quality differences such as changes in sensors,

type of controls, stage programming, and country

of origin specifications were also adjusted for in the hedonic indexes. The table

below provides a summary of mean price changes for microwave oven substitutions in both

the official and quality adjusted Major Appliances indexes.Summary of mean price changes for microwave oven substitutionsType of SubstitutionPublished Index NumberMean Price ChangeQuality Adjusted Index NumberMean Price ChangeAll Substitutions39+4.05 %39+1.31 %Comparable34+3.88 %18+1.42 %Quality Adjusted00.00 %21+1.22 %Non-comparable (Imputed)5+5.16 %00.00 %Substitution price change can be either “pure” (directly compared or quality

adjusted) or “imputed” (non-comparable). The empirical results above reveal that

not only was all “imputed” price change replaced with “pure” price

change in the quality adjusted index but that almost half of the “comparable”

substitution price changes in the published index were made “more comparable or

pure” in the quality adjusted index. In addition, the mean price changes for each

group of substitutions are lower after quality adjustment than in the published indexes.

This result implies that some price increases due to quality change may have been

reflected in the published indexes and caused them to be higher. Monthly price indexes were simulated for August 1999 through April 2000 to determine

the impact of quality adjusted microwave oven substitution price changes on the Major

Appliances CPI. First the published indexes, or without quality adjustment indexes,

were recreated by Statistical Analysis System (SAS) computer programs using historical CPI

data. The duplication of the published indexes provides a “control” environment

from which the quality adjusted Major Appliances indexes can be compared. U.S. level price indexes, such as those examined in this study, were obtained by

summing elementary, or local area, price indexes using aggregation weights derived from

the Consumer Expenditure Survey (CE). The results of the index simulation, with and

without hedonic quality adjustments, are presented in Attachment 5. In addition, graphical

representations of the simulated price indexes for Major Appliances are presented

in Attachments 1 and 6.Attachments 1 and 5 indicate that the U.S. CPI for Major Appliances would have

increased 0.6 percent instead of the official index increase of 0.8 percent if hedonic

quality adjustment methods had been applied to microwave oven (substitution) price changes

from August 1999 through April 2000. Given the small representation that microwave oven

substitution price changes had in the Major Appliances CPI during the study

period—an average of just four price quotes per month—the impact at the U.S. level was

relatively large. In addition, the empirical results suggest that the official index for Major

Appliances rose more rapidly than if hedonic quality adjustments had been applied to

microwave oven substitution price changes during the study period. Attachment 6 illustrates the differences between the published and quality adjusted

indexes on a monthly basis for the nine-month period in the study—August 1999 through

April 2000. Comparisons of the quality adjusted and published Major Appliances

price indexes reveal the following: In months when the index increased, the quality

adjusted index rose faster than the published index in one month (August), both indexes

rose at the same rate for two months (September and April), and the quality adjusted index

rose slower than the published index in the remaining two months (November and March). In

addition, in the remaining four months when the index fell, there were two months

(December and February) in which both indexes fell at the same rate and two months

(October and January) in which the quality adjusted index fell faster than the published

index. Two factors may account for the empirical results reported on in this study: First, the small number of microwave oven substitution price quotes that were quality

adjusted may have been to few to make a (representative) impact on the Major Appliances

indexes in 1999-2000. Microwave oven substitution price quotes accounted for less than two

percent—on average, four of 215 prices—of the monthly CPI sample for Major Appliances

from August 1999 to April 2000 and only half of these microwave substitutions had their

price changes adjusted using the hedonic technique. Second, CPI data collection procedures direct BLS field economists to select

substitution or replacement items that are the “same or similar” in quality as

the old item they had been pricing. This procedure tends to yield substitution price

quotes that have fewer bona fide characteristic changes (between substitute items)

than might have occurred if the procedures had instructed field economists to collect

(substitute item) data for the most technologically advanced or best selling microwave

ovens. This second factor is important in developing expectations as to the direction and

magnitude of quality adjusted indexes when compared to indexes without quality adjustments

for consumer appliance goods. If BLS field economists were instructed to substitute to the

best selling or most technologically advanced microwave oven products, one might expect

that the Major Appliances indexes with and without hedonic quality adjustments

would diverge further (than in this study) from each other. BLS is considering additional ways to more quickly bring a greater number of new good

quotes into the CPI rather than just relying on the current Telephone Point of Purchase

Survey (TPOPS) rotations. Lane (2000) provides a summary of additional methods for

bringing new goods into CPI samples more quickly.15 In particular, both the directed

item rotation and directed item replacement methods of updating price index

samples instruct field economists to “select a new set of (sample) items representing

a more recent period’s purchases” for target groups of goods or services that are

constantly changing in quality with successive generations of product introductions.Microwave Oven Characteristics That May Be Important in Future ModelsFuture generations of microwave ovens could experience rapid quality change if the

growth of “smart” appliances becomes popular with consumers. Recent studies

indicate that within ten years, 98 percent of (consumer) appliances will have computer

processing capability and be networked and controlled from remote locations—such as the

office or cell phone.16 The movement to embed networking capabilities into

consumer appliances for the home has been hailed as a major business opportunity for

appliance manufacturers, technology companies and (internet) service providers alike. To

date, however, these smart appliance products have been costly and used mainly in

demonstrations at trade shows and concept homes.17Currently, food scientists have created several smart microwave ovens that recognize

the food to be prepared and offer advice on recipes and nutrition. In particular, food

scientists maintain that the next generation of microwave ovens will incorporate the

following “smart” features: 18Microprocessors functioning as the “brains” of high-tech ovens.

Developed in collaboration with electronics manufacturer’s, the microprocessor will

control the oven’s electronics, such as turning the unit on for the correct length of time

and at the proper power setting. It will also be programmed to interpret and analyze food

science information, using the expert knowledge base of many food science professionals.

The smart microwave can inform you about ingredients and make recommendations to improve

your health.

Bar codes and scannerswill be the tools for transferring product

information into the microwave’s brain. Researchers are working with bar-code scanner

makers to develop two- and three-dimensional bar codes, which will be capable of storing

considerably more information than the current one-dimensional codes allow.

Voice recognitionwill allow consumers to customize the operation of

their appliance. For example, since the degree to which food is cooked varies with the

preference of the individual, the oven could be told to cook a steak until it is medium

rare rather than well done. Simply tell the microwave your name and the next time that

product is cooked, the microwave will modify the cooking instructions to your liking. Have

a food allergy? Are you diabetic? The microwave will check the ingredients against your

personal profile and send a warning if you shouldn’t be eating this food.

Internet accesswill keep microwave ovens informed on the latest cooking

instructions and nutritional information from web sites. Other internet oven features will

include warning consumers quickly about important news such as product recalls; letting

the microwave automatically send your grocery order to the supermarket each week; and

keeping track of food ingredients consumed for a report to your physician.

Specific examples of “smart” microwave ovens that have been developed to date

include the following:Sharp Electronics Corp. has developed a convection microwave oven that can

download recipes from the company’s Web site. The microwave then gives step-by-step

instructions on preparing the meal and automatically sets the time, adjusts the power and

does the roasting, baking, broiling or grilling. Sharp began selling its product in Japan

in October (1999) and hopes to introduce it in the U.S. in early 2001. Sharp’s new oven

sells for about $1,000 in Japan.19

has developed a microwave that reads directions on pre-packaged food

when the package’s bar code is swiped across a special sensor. The oven, developed with

Rutgers University researchers, will then contact the manufacturers’ Internet site, read

the directions and cook the meal. Samsung’s bar code-reading oven will likely cost less

than $500 when it hits the U.S. market sometime in early 2001.20Panasonic’s Virtual Chef Interactive Microwave oven can record a recipe from a

television cooking show or download it from the Internet, and then display it later for

consumer viewing on a screen. Or, on that same screen, you might input a list of the items

you have in your refrigerator and the microwave could suggest a recipe for using them.21

General Electric’s microwave oven voice-activated Advantium(TM) oven with

Speedcook technology that recognizes and responds to voice commands, understands 250

regional accents, can learn new languages, and can self-diagnose problems and alert the GE

Answer Center for parts and service.22General Electric’s microwave oven that reads Universal Product Codes (UPC) and

then automatically sets the proper cooking cycle, detects ingredients which consumers may

be allergic to, displays the calorie content of the dish, and can self-diagnose problems

and alert the GE Answer Center for parts and service.23

Many manufacturers and retailers of consumer appliances are optimistic that these

“smart” microwave ovens—and other “smart” appliances—will become

popular with consumers when they start to become available to U.S. consumers in early

2001. Their optimism is based, in part, on “the swift acceptance of the Internet

among consumers and because of the soon-to-be-widespread availability of so called

‘broadband’ internet access, where home users will have swift connections that eliminate

the delays and slow downloads of standard modem connections.” 24Many retailers are expected to aggressively advertise smart appliances when they become

available in the U.S. economy sometime in early 2001. For example, Sears intends to create

room settings inside many of the 860 full-line, mall-based Sears stores to explain to

consumers the value-added properties of these new (smart appliance) products and services.

In addition, these new smart appliance products will be demonstrated so consumers can

relate them to their own living rooms and kitchens. Recently, a spokesperson for Sears

indicated that the company “views the Internet as a huge catalyst that will drive

transformation in the home, and we intend to position ourselves to play whatever role is

necessary.” 25″Currently, the electronics industry is mulling over two emerging, would-be

standards for home networking of smart appliances, both based on software widely used in

personal computers and across the Internet. One of the home networking standards—known as

Universal Plug and Play (UPnP)—is being developed by a team of appliance hardware and

software manufacturers headed by Microsoft. The competing platform—a language from Sun

Microsystems called Jini—has the same goals as UPnP, which is to provide a standard for

networking home appliances. The first generation of both types of smart appliances should

be hitting the market in early 2001.”26In short, internet technology is making a whole new line of smart appliances a

possibility for consumers. However, these future smart appliances might hold some of the

same compatibility problems that computer users endure today. For example, one might be

able to turn on an Jini-equipped home security system with a Jini cell phone—but one

might not be able to power up an UPnP speaking microwave oven with it. Industry analysts

think that there will probably be bridges to connect the two platforms where customers

demand it. For example, one might have to work around a compatibility problem by using an

Jini-equipped cell phone to turn on your UPnP speaking microwave oven through a personal

computer that speaks both languages.27Technical issues aside, it seems clear that U.S. retailers will be bringing these new

smart appliances to the U.S. marketplace for consumer purchase in the very near future. If

smart appliances become popular with consumers when they are available for purchase, BLS

should try and include these new products in the Major Appliances CPI soon after

their introduction so that any rapid price movements—sometimes associated with the

introduction of new products—are not excluded from the CPI. Representation of smart

appliances in the Major Appliances CPI should be proportional to consumer

expenditures on these new products vis-à-vis consumer expenditures on all major

appliances. If consumer expenditures on smart appliances increase through time, so should

their representation in the CPI. ConclusionThe microwave oven hedonic model developed in this study represents a snapshot of how

the average consumer values quality for microwave ovens in today’s appliance market.

Iterative regressions for microwave ovens are included in this study to give the reader a

sense of hedonic model development as more categories of CPI characteristics were

considered for model inclusion. The current rate of (quality) change for this consumer

appliance product is not as fast as other retail products—for example, cellular and

wireless telephones or DVD players in the consumer electronics market. The parameter estimates in the final hedonic model for microwave ovens exhibit relative

robustness to the inclusion and deletion of other variables not included in the final

model. The direction and magnitude of the parameter estimates seem reasonable, and the

statistics pertaining to fit, significance and collinearity are within expected limits. It

should be used in conjunction with commodity analyst judgment to quality adjust CPI quote

level substitution data when possible. Future generations of microwave ovens could experience rapid quality change if the

growth of “smart” appliances becomes popular with consumers of this appliance.

BLS should include these new smart products in the Major Appliances CPI soon after

their introduction so that any rapid price movements—sometimes associated with the

introduction of new products—are not excluded from the CPI. Representation of smart

appliances in the Major Appliances CPI should be proportional to consumer

expenditures on these new products vis-à-vis consumer expenditures on all major

appliances.Notes Acknowledgments: the author wishes to thank Nicole Shepler, Walter Lane, Rick Devins and

John Greenlees for helpful suggestions.Silver (1998) notes that there are ” three different approaches to the use of

hedonic regressions for measuring quality-adjusted price changes. The first

complements the existing matched models approach generally used by statistical offices, by

helping to identify key quality characteristics and, when matches are not available,

providing adjustment factors to allow ‘like’ to be compared with

‘like’. The second is the direct method, found in the academic

literature, which uses the coefficients on the dummy variables for time in an hedonic

regression as estimates of quality-adjusted price changes. The third method

requires quite extensive data for the compilation of ‘exact’ hedonic price

indices as defined from economic theory.”—Page 1 from reference below. Source, “Raytheon Historical Backgrounder,” under the Microwave Cooking

heading on page 3; <>

Source, “Technology and Economic Growth in the Information Age,” National

Center for Policy Analysis, under the New Technologies Spread Faster heading on

page 6; http://www.ncpa.org/bg/bg147/bg147.html (accessed 3/21/2000).Source, “Toward A More Accurate Measure Of The Cost Of Living,” The Final

Report to the Senate Finance Committee of the Advisory Commission to Study the Consumer

Price Index,” under the New Products Bias heading on page 22;

http://www.ssa.gov/history/reports/boskinrpt.html (accessed 4/7/2000).Source, Cox and Alm (1997), “Time Well Spent: The Declining Real Cost of Living in

America,” Federal Reserve Bank of Dallas—1997 Annual Report; see Exhibit 8 on page

22; http://www.dallasfed.org/htm/pubs/pdfs/anreport/arpt97.pdf (accessed 12/8/1999). Source: “Microwave Ovens” in the Consumer Digest’s 2000 Annual Buying

Guide, November/December 1999, pages 106-107.For additional information about the hedonics project on quality change in the U.S. CPI

see Fixler, Fortuna, Greenlees and Lane (1999), “The Use of Hedonic Regressions to

Handle Quality Change: The Experience in the U.S. CPI,” Presented at the Fifth

Meeting of the International Working Group on Price Indices; August 1999; Pages 1-20.

http://www.statice.is/ottawa/bls.rtf (accessed November 1999).The collection of hedonic price data by CPI field economists coincided with the

collection of official CPI price data and TPOPS price data. Reports from the field

indicated that some respondents simply did not have the time to assist CPI field

economists with hedonic data collection.Source: “Microwave Ovens Test: Faster, smarter, bigger,” in Consumer

Reports December 1999 issue, page 28.Source: Shepler (2000) in “Developing a Hedonic Regression Model For Refrigerators

in the U.S. CPI,” under the Data and Regression Model http://www.bls.gov/cpirfr.htm

(accessed 8/16/2000)Source: “Measuring Prices in a Dynamic Economy: Re-Examining the CPI,” The

Conference Board, under the Quality Bias heading on page 19; Special Report

1260-99-SR, September 17, 1999.Source: “Microwave Ovens Test: Faster, smarter, bigger,” in Consumer

Reports December 1999 issue, page 30.Source: “Microwave Ovens Test: Faster, smarter, bigger,” in Consumer

Reports December 1999 issue, page 30.See Walter Lane, “Addressing the New Goods Problem in the Consumer Price

Index,” Presented at the Issues in Measuring Price Change and Consumption Conference,

Bureau of Labor Statistics, Washington, D.C., June 5-8, 2000, pages 1-26.Source: “GE Unveils Concept ‘Smart’ Appliances at NAHB,” Yahoo Finance—PR

Newswire; January 14, 2000, pp. 1-2; http://biz.yahoo.com/prnews/000114/ky_ge_new__1.html

(accessed January 19, 2000).Source: “Smart Appliances Hit The Net,” TechWeb News / Technology News;

January 18, 2000, pp. 1-3; http://www.techweb.com/wire/story/TWB20000118S0032 (accessed

May 5, 2000).Source: “New Wave Microwave,” Science and Technology News NetworkTm;

The Center for Science and the Media, and ScienCentral, Inc.; June 23, 1999, pages 1-4;

http://stn2.net/pagesl1/newwave/moreinfo.html (accessed 5/22/2000).Source: “Nukin’ meals on the Net,” USA Today—Tech Reviews; January 17, 2000,

pages 1-3; http://www.usatoday.com/life/cyber/tech/review/crg815.htm (accessed 5/11/2000).Source: “Nukin’ meals on the Net,” USA Today—Tech Reviews; January 17, 2000,

pages 1-3; http://www.usatoday.com/life/cyber/tech/review/crg815.htm (accessed 5/11/2000).Source: ” ‘Smart’ devices could raise machines’ IQ,” The Daily Camera; January

8, 2000, pages 1-2; http://www.bouldernews.com/business/08delec.html (accessed 5/30/2000).Source: “GE Unveils Concept ‘Smart’ Appliances at NAHB,” Yahoo Finance—PR

Newswire; January 14, 2000, pp. 1-2; http://biz.yahoo.com/prnews/000114/ky_ge_new__1.html

(accessed January 19, 2000). Also, “GE, Microsoft in pact for talking friges, smart

ovens,” Yahoo Finance; January 13, 2000, pages 1-2;

http://biz.yahoo.com/rf/000113/beg.html (accessed January 19, 2000).Source: “GE Unveils Concept ‘Smart’ Appliances at NAHB,” Yahoo Finance—PR

Newswire; January 14, 2000, pp. 1-2;

http://biz.yahoo.com/prnews/000114/ky_ge_new__1.html(accessed January 19, 2000). Also,

“GE, Microsoft in pact for talking friges, smart ovens,” Yahoo Finance; January

13, 2000, pages 1-2; http://biz.yahoo.com/rf/000113/beg.html (accessed January 19, 2000).Source: “Appliances to Be Linked to Internet,” Washington Post; January 18,

2000, pages 1-5; http://www.washingtonpost.com/wp-dyn/business/A57379-2000Jan17.html

(accessed May 5, 2000).Source: “Appliances to Be Linked to Internet,” Washington Post; January 18,

2000, pages 1-5; http://www.washingtonpost.com/wp-dyn/business/A57379-2000Jan17.html

(accessed May 5, 2000).Source: “Can Appliances Get Smart?” Washington Post; May 26, 2000, pages 1-3;

http://washingtonpost.com/wp-dyn/articles/A8164-2000May25.html (accessed May 26, 2000).Paraphrased from: “Can Appliances Get Smart?” Washington Post; May 26, 2000,

pages 1-3; http://washingtonpost.com/wp-dyn/articles/A8164-2000May25.html (accessed May

26, 2000).ReferencesConsumer Digest’s 1999 Annual Buying Guide (December 1998), pages 110-113.

Consumer Digest’s 2000 Annual Buying Guide (December 1999), pages 106-108.

Consumer Reports December 1999 Issue, pages 28-31.

Fixler, Fortuna, Greenlees and Lane (1999), “The Use of Hedonic Regressions to

Handle Quality Change: The Experience in the U.S. CPI,” Presented at the Fifth

Meeting of the International Working Group on Price Indices; August 1999; Pages 1-20.

http://www.statice.is/ottawa/bls.rtf (accessed November 1999).Silver, M.S. (1998), “An evaluation of the use of hedonic regressions for basic

components of consumer price indices,” Third Meeting of the International Working

Group on Price Indices, Statistics Netherlands, Voorburg: Netherlands (1998) 1-12.

http://www.statcan.ca/secure/english/ottawagroup/pdf/23SIL3.pdf (accessed November 1999).Lane, Walter (2000), “Addressing the New Goods Problem in the Consumer Price

Index,” Presented at the Issues in Measuring Price Change and Consumption Conference,

Bureau of Labor Statistics, Washington, D.C., June 5-8, 2000, pages 1-26.Attachment 1Attachment 2Number and Distribution of CPI Price Changes for Major

Appliances (HK01) and Microwave Ovens (HK014 – 01A)Major Appliances (HK01)     Total Prices CollectedSubstitutions# / (% of Total PricesComparable# / (% of Subs)Non-comparable# / (% of Subs)Month    990822736 / (16)19 / (53)17 / (47)990921727 / (12)22 / (81)05 / (19)991023333 / (14)30 / (91)03 / (09)991120816 / (08)11 / (69)05 / (31)991220915 / (11)09 / (60)06 / (40)000121322 / (10)17 / (77)05 / (33)000220808 / (04)07 / (88)01 / (12)000321019 / (09)14 / (74)05 / (26)000420920 / (10)19 / (95)01 / (05)Average21522 / (10)16 / (73)06 / (27)Microwave Ovens(HK014 – 01A    MonthTotal Prices CollectedSubstitutions # / (% of Total Prices)Comparable # / (% of Subs)Non-comparable # / (% of Subs)99084506 / (13)05 / ( 83) 01 / (17)99094006 / (15) 05 / ( 83)01 / (17)99105210 / (19)10 / (100) 0 99113704 / (11)03 / ( 75)01 / (25) 99123503 / (09)03 / (100)000013601 / (03)01 / (100)000023102 / (07)02 / (100)000033704 / (11)03 / ( 75)01 / (25)00043603 / (08)02 / ( 67)01 / (33)Average394.3 / (11)3.7 / (86)0.6 / (14)Attachment 3Iterative Regression 1Analysis of VarianceSourceDFSum of SquaresMean SquareF ValueProb>FModel494.7222323.68056445.3400.0001Error37720.046640.05317  C Total381114.76887   Root MSE0.23060R-square0.8253Dep Mean5.17114Adj R-sq0.8235C.V.4.45927  Parameter EstimatesVariableDFParameter EstimateStandard -Error^T for HO Parameter=0Prob>|T|ToleranceINTERCEP14.2760110.0825836351.7780.0001.Sale Price1-0.1551740.02463827-6.2980.00010.98764281Above Stove11.1065460.0281134939.3600.00010.95621038Capacity10.2669820.041583206.4200.00010.61155039Max Watt10.0003440.000103063.3340.00090.61034772Iterative Regression 2Analysis of VarianceSourceDFSum of SquaresMean SquareF ValueProb>FModel19100.867685.30883138.2470.0001Error36213.901180.03840  C Total381114.76887   Root MSE0.19596R-square0.8789Dep Mean5.17114Adj R-sq0.8725C.V.3.78953  Parameter EstimatesVariableDFParameter estimateStandard ErrorT for HO:Parameter=0Prob >|T|ToleranceINTERCEP14.4341620.0936578247.3440.00010.82343606Sale Price1-0.1079010.02293067-4.7060.00010.64537799Above Stove11.0026910.0290807734.4800.00010.78608449Capacity10.3379360.0311688510.8420.00010.28633282Amana10.4700440.103343434.5480.00010.46104201Emerson1-0.2182080.11875817-1.8370.06700.09690710GE10.2540410.093172902.7270.00670.32143698Goldstar1-0.0053430.10574798-0.0510.95970.06880676Kenmore10.0564830.092685780.6090.54260.19320499Panasonic10.0716790.097911010.7320.46460.25563210Samsung1-0.1463330.10209793-1.4330.15260.05643973Sharp10.0818460.089947540.9100.36350.21910637Whirlpool10.1948550.101085501.9280.05470.41832613Admiral1-0.1734840.11557959-1.5010.13420.43413066Frigidare10.0202320.122383690.1650.86880.69376954Hotpoint1-0.0878080.16679725-0.5260.59890.55326860Kitchenaid10.6661400.132421775.0300.00010.62584240Magic Chef1-0.1087360.14357889-0.7570.44930.43559856Maytag10.2215280.122177311.8130.07060.62782059Sanyo10.1400410.14335251-0.9770.3293 Iterative Regression 3Analysis of VarianceSourceDFSum of SquaresMean SquareF ValueProb>FModel16102.214306.38839185.7300.0001Error36512.554570.03440  C Total381114.76887   Root MSE0.18546R-square0.8906Dep Mean5.17114Adj R-sq0.8858C.V.3.58648  Parameter EstimatesVariableDFParameter EstimateStandard ErrorT for HO:Parameter=0Prob > |T|ToleranceINTERCEP14.5257270.04205034107.6260.0001.Sale Price1-0.1002070.02051750-4.8840.00010.92125545Above Stove10.9791980.0255729738.2900.00010.74753072Capacity10.3164390.0288195810.9800.00010.82357154Amana10.4062240.053468207.5970.00010.95810121Emerson1-0.2777170.07782490-3.5680.00040.96160350GE10.2025660.030505916.6400.00010.80971564Samsung1-0.1837020.05186828-3.5420.00040.88717910Whirlpool10.1516050.048360703.1350.00190.85745856Admiral1-0.2293260.07260729-3.1580.00170.94947271Kitchenaid10.5544010.094645945.8580.00010.97009987Maytag10.1933760.080749392.3950.01710.89321220Sanyo1-0.1839750.10843536-1.6970.09060.98281091Manual Ctrl1-0.1963390.04476733-4.3860.00010.905547624 Stage10.1299280.028134204.6180.00010.883344223 Stage1-0.0376730.02421545-1.5560.12060.852632112 Stage1-0.0302320.03383483-0.8940.37220.89913171Iterative Regression 4Analysis of VarianceSourceDFSum of SquaresMean SquareF ValueProb>FModel18103.292245.73846181.5040.0001Error36311.476630.03162  C Total381114.76887   Root MSE0.17781R-square0.9000Dep Mean5.17114Adj R-sq0.8950C.V.3.43849  Parameter EstimatesVariableDFParameter EstimateStandard ErrorT for HO:Parameter=0Prob > |T|ToleranceINTERCEP 14.5936080.0479261095.8480.0001.Sale Price 1-0.0933310.01974323-4.7270.0001 0.91451638Above Stove 10.8782950.0342591725.6370.0001 0.38285716Capacity 10.3245390.0279827211.5980.0001 0.80296292Amana 10.4251510.051539598.2490.0001 0.94780636Emerson 1-0.2676390.07479585-3.5780.0004 0.95692316GE 10.1691770.030054115.6290.0001 0.76681679Samsung 1-0.1804040.04962886-3.6350.0003 0.89072827Whirlpool 10.1537330.046200273.3280.0010 0.86359135Admiral 1-0.2295150.06981933-3.2870.0011 0.94382304Kitchenaid 10.5246480.091402385.7400.0001 0.95610239Maytag 10.1764210.078140332.2580.0246 0.87676176Sanyo 1-0.1966330.10410684-1.8890.0597 0.98005893Manual Ctrl 1-0.1917670.04333815-4.4250.0001 0.888161494 Stage 10.1230060.026093894.7140.0001 0.94388785BI Sensor 10.1004760.027142953.7020.0002 0.84849621Recess Tray1-0.0391210.02278787-1.7170.08690.85301826Rotate Tray1-0.0994920.03339411-2.9790.00310.86946641Remove Rack10.1223490.038617303.1680.00170.38830801Iterative Regression 5Analysis of VarianceSourceDFSum of SquaresMean SquareF ValueProb>FModel23104.745534.55415162.6590.0001Error35810.023340.02800  C Total381114.76887   Root MSE0.16733R-square0.9127Dep Mean5.17114Adj R-sq0.9071C.V.3.23578  Parameter EstimatesVariableDFParameter estimateStandard ErrorT for HO:Parameter=oProb > |T|Toleran

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