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.

Answer 1

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