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Consumer Price Index
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A goal of this project was to attempt to collect data that was more technical innature, it was believed that this data would prove useful in producing models
William Thompson
Background
The Bureau of Labor Statistics (BLS) is continuing with its research effort to improve the estimation of quality change for selected items in the Consumer Price Index (CPI). Some experts believe that the CPI overstates the rate of inflation for products that are rapidly improving in quality. Unfortunately a measure of quality-adjusted price change faced by consumers cannot be directly observed in the marketplace. Hedonic regression analysis, however, offers one way to estimate price values for individual characteristics of an item. The estimated price values can then be used to differentiate between pure price change and price change due to quality differences between old and replacement items in the CPI sample. If we are successful in the modeling effort, we can account for a greater number of price changes realized by consumers even when new product introductions are marked by technological improvements.
The inclusion of the video cassette recorder (VCR) in this research effort is linked to the perception that there may be some quality bias in the price index for this item. Also, the success of earlier hedonic research for VCRs suggests that VCRs should be included in the continuing effort to develop hedonic regression models for the purpose of adjusting for quality change in the CPI index.
The VCR was introduced twenty-five years ago and has become a staple in American households. The market place for VCRs is populated by a relatively large number of brands and a vast number of models with numerous features and characteristics. The purpose of this research is to identify VCR features and characteristics that are valued by the consumer and determine how they contribute to the market price of the product. Using hedonic regression analysis, parameter estimates are developed that serve as an indication of the relative price value of specific features or characteristics in the overall price of the VCR. The VCR data consist of current CPI data, as well as special pricing observations to augment the CPI sample and add robustness to the research effort. The data were collected by CPI representatives, and information on the items was supplemented by secondary sources, including Internet sites, consumer magazines, and manufacturer advertisements.
The Modeling Process
The sample of VCR prices used in monthly CPI estimation was insufficient for regression modeling purposes. Based on current CPI sampling procedures, CPI statisticians designed a supplemental sample for hedonic modeling purposes only. The new sample added 296 observations in addition to the 243 observations from the CPI sample. The final sample included 217 specially collected observations and 243 observations from the CPI sample. The field data collectors were unable to collect data for 26 percent of the supplemental sample. Observations with inconsistent or incomplete data and for which no manufacturer model number could be found were dropped from the data set.
To collect data for VCRs CPI data collectors use data collection forms known as checklists, which outline the product characteristics judged to be most important. When the CPI representative completes the data collection form we get a description indicating all the pertinent characteristics and the price of the item. (See Attachment A for the RA031 Cluster 01A, Video Cassette Players/Recorders data collection form.) Collecting data for electronic goods is not a simple task. Manufacturers and retailers use confusing terminology and often use different names for the same feature. Consumers are left to ask sales personnel for assistance to decipher technical information. Some of these difficulties spill over into CPI data collection efforts. Where there were inconsistencies or incompleteness in the data collected for this research effort, the manufacturer model numbers obtained by CPI data collectors were matched to specifications provided by the manufacturer Internet sites.
Although most VCRs are indeed capable of recording as well playback, there are units on the market which are playback only. There were a total of thirteen player-only units in the sample. There was an unsuccessful attempt to include unit type (player or play/recorder) in the model; however the t-statistic did not come close to a reasonable level of acceptance. The mean price for play only units was $126.50 compared to a mean price of $195.26 for play/record units. These play-only observations were deleted from the final data set, as it appears that the pricing structure for player-only units is different than that of units that have recording ability.
Tape format is dominated by the Video Home System (VHS), VHS High Quality (VHS-HQ) or Super VHS (S-VHS); the latter offers the best among analog formats, with 50 percent more picture sharpness than standard VHS. The beta system, which was the early competitor to VHS, is used primarily for commercial applications. The 8mm players are relegated to use by those with 8mm camcorders that do not have converter with which to watch their 8mm camcorder tapes on VHS. Finally, Digital VHS (D-VHS) first introduced in 1998 and designed to be a partner with DirecTVSatellite System or the Dish Network, has not yet achieved mainstream acceptance.
As expected, the sample proved to be skewed: While VHS had observations split between VHS and S-VHS, there were no observations for beta tape, two observations for 8 mm and one observation for digital. The digital and 8 mm observations were deleted from the sample to allow focus on the more popular VHS and Super VHS formats. There seems to be no discernible difference between VHS and VHS-HQ. Manufacturer reporting of this information was inconsistent, and it became clear that consumers would have difficulty in discerning if the units they were purchasing were equipped with HQ. Instead VHS and VHS-HQ variables were combined, so by default, tape format was either VHS or Super VHS. Since VHS made up an overwhelming majority of the sample it was chosen as the base variable for this category.
Brand was dominated by four companies: Sony, Panasonic, JVC and RCA, which combined made up 61 percent of the sample. Of the other 21 brands named, no other brand made up more than five percent of the sample. Sony and JVC (which combined made up 31 percent of the sample) were included in the model along with Zenith (five percent) and Proscan ( two percent). Thus, 38 percent of the brands by volume of sales were explicitly included as variables in the model. By implication brands not included in the model were grouped into a miscellaneous "Other" category and designated as a variable. The direction and magnitude for each of the included specifications met a priori expectations.
There is a direct relationship between the number of heads a VCR has and the quality of the picture during playback, thus number of heads is a fundamental attribute of the VCR. Most of the observations consisted of units with four heads, approximately 93 percent of the sample. VCRs with two heads comprised approximately six percent and VCRs with six heads made less than one percent. Although only a small percentage of the sample had two or six heads, the corresponding variables proved to be statistically significant and met expectations in terms of magnitude.
Hi-fi stereo units made up 81 percent of the sample, while mono-sound comprised 16 percent and surround sound two percent of the sample. With stereo sound as the base variable in the category, the mono-sound variable displayed the expected direction and magnitude and proved to be significant. The results for the surround sound variable were not as anticipated and did not prove to be significant.
The variable dual tape well represents the feature of dual tape capability, which allows the consumer to record tapes in addition to television shows. This feature is associated exclusively with the GO Video brand. Despite only a few observations, this variable proved to be large in terms of magnitude and significance. The GO Video brand has invested heavily not only in the technology but also the legal concerns of exclusively manufacturing a "dual well" machine. Thus, the dual-well VCR is a high-end type of VCR.
Other features that were included as variables in the model were flying erase head which permits smoother editing of tapes, the capability to advance through commercials or omit commercials when recording, and "VCR plus " recording, which allows the consumer to program the VCR to record a particular show using a five digit code.
A disappointing result of the modeling process was that the lines of horizontal output, a measure of the quality of the picture produced, (the more lines the higher the quality), could not be included in the model. Initially it was anticipated that the lines of horizontal output would be fruitful; however, due to the technical nature of the information and the inconsistency in its availability there was a low rate of successful data capture. So while lines of horizontal output may be an important technical characteristic, it remains unclear if and how consumers value this characteristic, especially if they are unable to determine the lines of output for their unit. A couple of other characteristics that may have suffered similar plights are Quasi S-VHS playback, and multiple format conversion. Some common characteristics that did not prove significant include automatic rewind, automatic head cleaner, child lock, and automatic clock set. Remote and manufacturer warranty also did not prove to be significant.
Country of origin was a new collection initiative. Japan made up most of the sample at 42 percent, while 31 percent of the sample came from other countries in the Far East. The remaining sample came from Mexico (seven percent) and the U.S. A. (three percent), while in 17 percent of the observations the country of origin was not available. While country of origin was given considerable attention the modeling results offered no compelling reason to include country of origin as a variable.
Statistical results of the model are presented in the table below:
VCR Model
|
Variable Name |
Parameter Estimate |
T-statistic |
Variable Name |
Parameter Estimate |
T-statistic |
| Intercept |
4.98933 |
162.667 |
Other: | ||
| Last price was sale |
-0.10264 |
-3.886 |
Dual well deck |
1.20147 |
12.572 |
| Type: | Flying head edit feature |
0.80020 |
9.149 |
||
| Super VHS |
0.49856 |
9.789 |
Commercial skip/advance |
0.09392 |
3.676 |
| VHS |
Base |
Inputs front & back |
0.29095 |
7.256 |
|
| Brand: | VCR plus |
0.08967 |
3.453 |
||
| Proscan |
0.23676 |
2.897 |
Cable/satellite control |
0.04516 |
2.022 |
| Sony |
0.21914 |
7.395 |
Type of Business Variables | ||
| JVC |
0.07943 |
2.035 |
Appliance |
0.09483 |
2.759 |
| Other brands not listed |
Base |
Electronic |
0.09096 |
3.078 |
|
| Zenith |
-0.12257 |
-2.335 |
Discount Department |
-0.06642 |
-2.191 |
| Audio: | Warehouse |
-0.13498 |
2.759 |
||
| Hi-fi stereo |
Base |
||||
| Mono Sound |
-0.19545 |
-6.108 |
|||
| Number of heads | Region Variables | ||||
| Six video heads |
0.24494 |
2.012 |
Midwest Region |
-0.03334 |
-1.370 |
| Four video heads |
Base |
||||
| Two video heads |
-0.27807 |
-6.218 |
|||
|
N=439 R2=0.7581 Adjusted R2=0.7466 F Statistic=65.661 |
|||||
The R-squared of .7581 says that almost 76 percent of the variation in the dependent variable is explained by the independent variables. This result compares to the Liegey and Shepler hedonic model which had an R-squared value of 95 percent.(1) (See Attachment C.) Although the hedonic models are similar in terms of types of variables included in the model, the Liegey and Shepler model is clearly more encompassing in terms of features characteristics, brand name and type of player. Although a comparison between the two hedonic models may provide some insights and topics for debate, any comparison should tempered by an understanding of the differences in approach for these two modeling efforts.
The model developed in this research was based on consumer retail offer prices and characteristics collected by CPI representatives. The Liegey and Shepler research was based exclusively on data obtained from the Consumer Digest 1998 Annual Buying Guide. In addition to the fact that these data are less current that the data used here, there is a theoretical concern that the list prices such as those listed in the Consumer Digest do not reflect prices that the consumer faces in the marketplace.(2) Using list prices that do not equal consumer retail offer prices may give a higher R-squared value but provide for a less accurate hedonic model. If this concern is true then it would be difficult to compare a hedonic model based on consumer retail offer prices and a hedonic model based on list prices. Also complicating comparisons between the two approaches is that the Liegey and Shepler model is unable to account for the price effects of the type of business, the region of the country or size of a city.
Comparing Quality Adjusted and Published Indexes
Simulating an index with quality adjusted VCR substitutions will illustrate the impact of using the VCR regression model in calculating the CPI. The published index (without quality adjustments) is recreated with CPI historical data. This recreation is then compared to the simulated index that includes quality-adjusted substitutions. The simulation of the published and quality adjusted indexes covers the time period from May 1999 to December 1999. Index price changes for the U.S. city level, such as those examined in this study, were obtained by summing price changes over all (elementary) index areas using aggregation weights derived from the Consumer Expenditure Survey.
VCRs are included in the Other video equipment item stratum (RA031) along with camcorders, DVD players, satellite video products and other miscellaneous video products. VCRs have an estimated 46 percent of the weight within Other video equipment. During the time period from December 1997 to December 1999 the Other video equipment index decreased 26.5 percent. The average monthly decline was 1.1 percent. The Other video equipment index was redefined for the January 1998 CPI revision so a longer term comparison is not available. Prior to the revision, VCRs were included in the Video products other than televisions index. This index decreased 38.7 percent from December 1988 to December 1997 — an average monthly decline of 0.4 percent.
For the time period June 1999 to December 1999 Other video equipment had a total of 1589 quotes priced. Over this time period there were 224 substitutions for an average substitution rate of 14 percent. Of the 224 substitutions, 99 substitutes, or 44 percent, were deemed to be 'comparable', meaning that 56 percent of the substitutes were coded as non comparable and were included for index calculation using the 'class-mean imputation' method.(3)
For VCRs alone there were a total of 130 substitutions during the June to December time period. In the published index 51 percent of the VCR substitutions directly compared the price of the price of the new item to the price of the previous item. There was one observation coded as quality adjusted. The quality adjustment for this observation was not based on parameter estimates from a hedonic model; the quality adjusted price was determined by the analyst from information received from the representative. Finally, price changes for the remainder of the substitutions were imputed using the class-mean imputation method.
For the purpose of calculating the quality adjusted index all the substitutions were reevaluated. One of the benefits of using a hedonic model in evaluating substitutions is that the analyst has an opportunity to review price data and item characteristics with a statistical tool, thus enabling him/her to render judgments based on statistics rather than expert judgment alone. A direct result of this benefit was that the method of price change for 64 percent (up from 51 percent for the published index) of the substitutions used the direct comparison between the price of the new item and the price of the old item. Twenty-seven percent of the substitutions were deemed to have changes in quality that could be adjusted using the hedonic model results. Only nine percent of the substitutions continued to use the class mean imputation method. The quality adjusted index had an overall comparability ratio of 91 percent compared to 52 percent for the published index. The use of the hedonic model to reevaluate substitutions impacts the index in two ways: 1) via substitutions that are quality adjusted; and 2) through substitutions that with additional information provided by the model can be directly compared rather than use the class mean imputation method. From the table below the mean price change for directly comparable quotes went from a negative 3.72 percent to a negative 1.00-percent.
VCR Substitutions from June 1999 to December 1999
|
Published Index Mean price Number Percentage Change |
Quality Adjusted Index Mean price Number Percentage Change |
|
| All substitutions | 130 100% -4.30 | 130 100% -1.26 |
| Directly compared substitutions | 67 51% -3.72 | 83 64% -1.00 |
| Quality Adjusted |
1 1% -9.10 |
35 27% -1.41 |
| Class mean imputed
(noncomparable) substitutions |
62 48% -4.35 | 12 9% -1.85 |
Graphic presentations of the results of the RA031 index simulation, with and without hedonic quality adjustments, are shown in Attachment B. The first graph shows a line graph of index levels for the published and quality adjusted indexes from May 1999 to December 1999. The second graph illustrates the differences for one-month changes between the published and quality adjusted indexes.
From May 1999 to December 1999 the quality adjusted index decreased 6.7 percent compared to a 7.7-percent decrease for the published index.(4) The differences, quality adjusted minus published, for the one-month changes ranged from a low -0.72 percentage point to a high of 1.33 percentage point. The average difference for the seven month time period was 0.15 percent. These results show that the CPI may have been overstating the rate of price decline for item category of Other video equipment. That is, if the CPI actually had used the regression model for VCRs, the index would have had a smaller decline than the CPI actually shows.
The results of this study are not surprising given that Liegey and Shepler had a similar although smaller difference (0.1 percent difference over a 12 month study) between the published index and the quality adjusted index. Additionally, Kokoski, Waehrer, and Rozaklis found similar results (1.7 percent difference over a 12 month study) for some audio products.(5) Just as the Liegey and Shepler research was based on data from non-CPI sources, the Kokoski, Waehrer and Rozaklis research was based on point-of-sale data purchased from NPD, a private firm specializing in the collection and marketing of such data for sale. NPD data more closely resembles CPI data than the Consumer Digest's list price data, but differs in that NPD data covers a significantly wider product range than CPI data. Although there are differences in the source of the data the index simulation results can not be totally discounted.
It is clear the VCR is no longer a new, high tech consumer good, since 93 million U.S households own at least one VCR, according to industry sources. As Liegey and Shepler point out, the issue for the VCR index is not to capture falling prices that a high-tech consumer good faces early in it's product cycle; rather, the VCR index faces the quality and price change issues as they relate to a mature product.(6)
Conclusion
It is unclear what the future holds for the VCR. It is likely that the VCR will continue to be popular in the near term. While someday in the future the VCR or at least the VHS format will give way to some type of digital format, recent VCR sales have hit record numbers. 1998 was a banner year for VCR sales, up eight percent from the previous year, and the second consecutive record breaking year.(7) If the DVD does develop the technology to record and continues its downward price trend then it is very likely that the DVD player will make the VCR obsolete at some point in the future.
The CPI will begin to use hedonic regression models for VCRs beginning in April 2000.
Given the technological evolution of the consumer electronic market, in which VCRs exist, it is likely that this model will not prove to be completely stable. CPI intends to test the stability of the model using new data in the near future.
Notes
(1) Paul Liegey and Nicole Shepler, "Adjusting VCR Prices for quality change: a study using hedonic methods," Monthly Labor Review, September 1999, page 13. (2) Liegey and Shepler, footnote 20, page 32. (3) See Marshall B Reinsdorf, Paul Liegey, and Kenneth J. Stewart, "New Ways of Handling Quality Change in the U.S. Consumer Price Index," BLS working Paper no. 276 (Bureau of Labor Statistics 1996). (4) In addition to quality adjusting the VCR substitutions, some of the impute price changes for the class-mean substitutions (the noncomparable substitutions) in the Other Video Equipment index were recalculated since the inclusion of the quality adjustments changed the information used in calculating the imputations. (5) Mary Kokoski, Keith Waehrer, and Patricia Rozaklis, "Using Hedonic Methods for Quality Adjustment in the CPI: The Consumer Audio Products Component," BLS draft paper 1999, p. 11. (6) Paul Liegey and Nicole Shepler, "Using Hedonic Methods to Quality Adjust VCR Prices: a Study Using Hedonic Methods," Monthly Labor Review, September 1999, pp. 23-24. (7) http://www.ce.org, visited on Jan12, 2000.ATTACHMENT A
BUREAU OF LABOR STATISTICS U.S. DEPARTMENT OF LABOR CONSUMER PRICE INDEX - ELI CHECKLIST______________________________________________________ collection outlet quote arranging period: __ __ __ __ number: __ __ __ __ __ __ __ code: __ __ __ code: __ __ __ __ _________________________________________________________________________________________ ELI No./ cluster title RA031 OTHER VIDEO EQUIPMENT code 01A item availability: 1-AVAILABLE 2-ELI NOT SOLD 3-INIT INCOMPLETE purpose of checklist: 1-INIT 2-INIT COMPL 3-SPEC CORR 4-SUB 5-REINIT 6-CHECK REV _________________________________________________________________________________________ CURRENT PERIOD | SALES TAX | price _ _ _ _ _ _ . _ _ _ | included: YES NO | type of price: REG SALE | | |____________________________________________ | YEAR-ROUND | in-season: JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC ____________|____________________________________________________________________________ respondent: location: _________________________________________________________________________________________ field message: _________________________________________________________________________________________ CLUSTER 01A - VIDEO CASSETTE PLAYERS/RECORDERS TYPE MANUFACTURER'S MODEL NUMBER A1 Player Only A2 Player/Recorder D99 ______________________________ TAPE FORMAT NUMBER OF VIDEO HEADS B1 VHS E1 Two B2 VHS HQ E2 Three B3 Super VHS (S-VHS) E3 Four B4 Beta E4 Five B5 Extended Definition Beta (ED Beta) E5 Six B6 8mm E99 Other, B7 Hi 8mm B8 Digital VHS (D-VHS) ______________________________ B9 Digital Video (DV) B99 Other, LINES OF HORIZONTAL OUTPUT ______________________________ F99 ______________________________ BRAND AUDIO CAPABILITIES C1 Emerson G1 Surround Sound C2 Fisher G2 Hi-Fi Stereo C3 GE G3 Monaural C4 Hitachi H99 Other audio capability, C5 JVC C6 Mitsubishi ______________________________ C7 Panasonic I99 Other audio capability, C8 Philips/Magnavox C9 Proscan ______________________________ C10 RCA C11 Samsung C12 Sanyo C13 Sharp C14 Sony C15 Toshiba C16 Zenith C99 Other, ______________________________
RA031-01A - VIDEO CASSETTE PLAYERS/RECORDERS - CONTINUED GENERAL FEATURES OTHER FEATURES J1 Dual well deck, both record and AG1 Front panel Audio/Video inputs playback AH99 Other, J2 Dual well deck, one record and one playback ______________________________ K1 Quasi S-VHS Playback AI99 Other, L1 Multiple format conversion M1 Flying Erase Head ______________________________ N1 Automatic Rewind AJ99 Other, P1 Automatic Head Cleaner Q1 Cable and/or satellite dish ______________________________ channel control R99 Other general feature, WARRANTY AK1 One year parts and labor ______________________________ AK2 Two years parts and labor AK3 Three years parts and labor PROGRAMMING FEATURES AK99 Warranty, other type, S1 On screen program guide T1 Commercial Skip ______________________________ U1 Commercial Advance V1 Skip Search COUNTRY OF ORIGIN W1 Index Plus AL1 Not Available X1 VCR Plus + Recording AL2 United States Y1 Child Lock AL3 Japan AA1 Automatic Clock Set AL99 Other, AB1 Movie Advance AC99 Other programming feature, ______________________________ ______________________________ OTHER PRICE FACTORS REMOTE CONTROL BA99 ______________________________ AD1 Controls VCR only AD2 Controls same brand TV BB99 ______________________________ AD3 Controls other brand TVs AE1 Illuminated Remote BC99 ______________________________ AF99 Other remote control feature, ** OTHER CLARIFYING INFORMATION ______________________________ CA99 ______________________________ CB99 ______________________________ CC99 ______________________________ _________________________________________________________________________________________ BLS 3400B (Rev. February 1995) RA031 page 3 of 16 Revised April 1999
DEFINITION OF TERMS CLUSTER 01A-VIDEO CASSETTE PLAYERS/RECORDERS 8mm - Eight millimeter is a type of video tape. AUTOMATIC CLOCK SET - The VCR reads instructions from a broadcast signal that allows the VCR to set its own clock. AUTOMATIC HEAD CLEANER - The machine is able to clean its own video heads. AUTOMATIC REWIND - The tape rewinds automatically after play is complete. BETA - Type of tape. Rare in consumer applications. Do not price a professional model. CABLE AND/OR SATELLITE DISH CHANNEL CONTROL - When the VCR is programmed to record over a cable or satellite system, it is able to set the cable or satellite system to the correct channel for recording. CHILD LOCK - Freezes control of VCR except for timer functions. COMMERCIAL ADVANCE - The VCR marks sections of commercials electronically and fast forwards through them automatically during playback. COMMERCIAL SKIP - The VCR omits commercials while recording. DIGITAL VHS (D-VHS) - The video is stored in digital format on the VHS tape rather than as an analog tape. DIGITAL VIDEO (DV) - A particular standard for storing digital video information used in VCRs and Camcorders. DUAL WELL DECK - There are two places in the chassis of the VCR (wells) to input tapes. Some types may permit recording in either of the wells. EXTENDED DEFINITION BETA (ED BETA) - A system used in the Beta tape format which provides superior video quality versus "standard" definition Beta. FLYING HEAD ERASE - A special head mounted on the same spinning headwheel as the recording heads that allows the VCR to create edited tapes with smoother transitions than would be possible otherwise. FRONT PANEL AUDIO/VIDEO INPUT - There is a place on the front panel of the VCR where video input from another source such as a video camera or video game can be connected. HI-BAND 8mm (HI8 8mm) - A system used in eight millimeter tape format which provides superior video quality versus "standard" eight millimeter. HiFi STEREO - The VCR will decode and output two channels of audio information (stereo). INDEX PLUS - May create an on-screen listing of taped programs along with date recorded and running time. Fast forwards to a selected program and plays it.
ATTACHMENT B
ATTACHMENT C
Liegey and Shepler VCR Model
|
Variable name |
Parameter Estimate |
T-statistic |
Variable name |
Parameter Estimate |
T-statistic |
| Intercept |
5.12849 |
179.013 |
Number of heads: | ||
| Type: | Two video heads |
-0.10864 |
-3.449 |
||
| VHS Player |
-0.13886 |
-3.053 |
Four video heads |
Base |
|
| VHS |
Base |
Six video heads |
0.48777 |
6.279 |
|
| Quasi SVHS |
0.09705 |
1.877 |
Other: | ||
| SVHS |
0.71605 |
16.697 |
Auto rewind |
0.12569 |
5.895 |
| Dual deck VCR |
0.89027 |
17.211 |
Cable channel changer |
0.12856 |
5.540 |
| Multi format converter |
1.38890 |
12.955 |
Child lock |
0.03977 |
2.002 |
| Brand: | Commercial advance |
0.17805 |
5.889 |
||
| Marantz |
0.59280 |
7.445 |
Commercial skip |
0.11848 |
4.748 |
| Sony/Toshiba/Mitsubishi |
0.22754 |
7.559 |
Flying head edit feature |
0.27088 |
7.539 |
| Proscan |
0.15815 |
2.337 |
Automatic head cleaner |
0.03369 |
1.503 |
| Other brands not listed |
Base |
Hi-fi stereo |
0.19133 |
9.333 |
|
| Funai/Phillips/Symphonic |
-0.17155 |
-5.839 |
Index plus |
0.25869 |
2.356 |
| Samsung |
-0.23819 |
-5.757 |
Skip search |
0.17100 |
6.988 |
| Starsightâ |
0.56336 |
9.431 |
|||
| VCR plus |
0.12219 |
5.537 |
|||
|
N = 176 R2 = 0.9581 Adjusted R2 = 0.9514 F statistic = 143.746 |
|||||
Last Modified Date: October 16, 2001