Question

10. 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 (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Brand	Price (X)	Score (Y)
Dell	2800	60
Hisense	2800	55
Hitachi	2700	45
JVC	3500	50
LG	3300	55
Maxent	2000	38
Panasonic	4000	67
Phillips	3000	56
Proview	2500	32
Samsung	3000	40

Use the above data to develop and estimated regression equation and interpret 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 $3800. Test the significance of slope coefficient.

Answer 1

The estimated regression equation is predicted score =8.895 +0.014 (Price)

Interpretation: For an unit increase in price , there will increment in score by 0.014 units which implies as price score increases

Coefficient of determination: 0.491

Correlation coefficient: 0.701

We get square of correlation coefficient (r²) as the coefficient of determination (R)

49.1 ℅ of variation in the score is explained by price of the TV

The overall score for a 42-inch plasma TV with price $3800 is 62.095

Null Hypothesis,H₀ : Slope coefficient is zero

Alternative Hypothesis , H₁: Slope coefficient is not zero

Level of significance = 0.05

Test statistic :

The value of t is 2.777

p value is .024

Since p value is less than 0.05 , we reject H₀ and conclude that price affects score significantly.