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	2900	50
Hisense	2800	52
Hitachi	2700	45
JVC	3500	60
LG	3300	56
Maxent	2000	30
Panasonic	4200	68
Phillips	3100	56
Proview	2500	35
Samsung	3000	48

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 $3400. Finally, test the significance of the slope coefficient. (Note that you need to answer all parts of the question and provide necessary interpretations to get full points).

Answer 1

i have comple this problem with the help of R software

the r code are given below

x=c(2900,2800,2700,3500,3300,2000,4200,3100,2500,3000)
> x
[1] 2900 2800 2700 3500 3300 2000 4200 3100 2500 3000
> y=c(50,52,45,60,56,30,68,56,35,48)
> y
[1] 50 52 45 60 56 30 68 56 35 48
> model=lm(y~x)
> model

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
-4.33962 0.01811

> summary(model)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-5.943 -1.972 0.500 1.594 5.623

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.339623 6.367015 -0.682 0.515
x 0.018113 0.002086 8.684 2.41e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.72 on 8 degrees of freedom
Multiple R-squared: 0.9041, Adjusted R-squared: 0.8921
F-statistic: 75.41 on 1 and 8 DF, p-value: 2.408e-05

> residuals=model$residuals
> residuals
1 2 3 4 5 6 7
1.8113208 5.6226415 0.4339623 0.9433962 0.5660377 -1.8867925 -3.7358491
8 9 10
4.1886792 -5.9433962 -2.0000000
> predictedscore=model$fitted
> predictedscore
1 2 3 4 5 6 7 8
48.18868 46.37736 44.56604 59.05660 55.43396 31.88679 71.73585 51.81132
9 10
40.94340 50.00000