. Consumer Reports provided extensive testing and ratings for more than 100 HDTV
ID: 3372169 • Letter: #
Question
. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data changed here):
Brand
Price
Score
Dell
2800
49
Hisense
3000
54
Hitachi
2700
45
JVC
3500
55
LG
3500
57
Maxent
2000
29
Panasonic
4000
70
Phillips
3000
55
Proview
2500
32
Samsung
3000
54
Use the above data to develop and estimate regression equation. Interpret the results. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600.
Brand
Price
Score
Dell
2800
49
Hisense
3000
54
Hitachi
2700
45
JVC
3500
55
LG
3500
57
Maxent
2000
29
Panasonic
4000
70
Phillips
3000
55
Proview
2500
32
Samsung
3000
54
Explanation / Answer
Regression Analysis: score versus price
Model Summary
S R-sq R-sq(adj) R-sq(pred)
4.55517 87.44% 85.87% 82.26%
Coefficients
Term Coef SE Coef T-Value P-Value
Constant -10.10 8.18 -1.24 0.252
price 0.02003 0.00268 7.46 0.000
Regression Equation
score = -10.10 + 0.02003 price
coefficient of determination = 0.8744 = 87.44%
correlation coefficient = sqrt(0.8744) = 0.9351
The square of correlation coefficient is Coefficient of Determination.
Coefficient of Determination is proportion of variation in dependent variable y i.e Score.
price = 3600
score = -10.10 + 0.02003 price
score = -10.10 + 0.02003 * 3600
Score = 62.008
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