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 (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	2900	55
Hisense	2800	54
Hitachi	2700	45
JVC	3500	56
LG	3300	54
Maxent	2000	35
Panasonic	4200	68
Phillips	3100	56
Proview	2500	32
Samsung	3000	45

Use the above data to develop and estimated regression equation and interpret the coefficients. 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 $4000. Finally, test the significance of the slope coefficient. (Note that you need to provide necessary interpretations to get full points).

Answer 1

Intercept = 2.26 which can be interpreted as the minimum score for TV for zero price is 2.26

Slope = 0.01591 which can be interpreted as for unit dollar increase in price the score of the TV increases by 0.01591 units.

Coefficient of determination= r^2 where r us correlation coefficient.

Coefficient of determination = 0.7653

Correlation coefficient = 0.8748

76.53% of the variation in the score Y is explained by the fitted model for given prices.

The estimated score for TV of price:

Test of significance of regression coefficient i. e. Slope

Thus it may concluded that there is significant relationship between price and score of the TV.

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