1. Consumer Reports provided extensive testing and ratings for more than 100 HDT
ID: 3054422 • Letter: 1
Question
1. 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 (The actual Consumer Report data changed here arbitrarily):
Brand
Price
Score
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 the slope and intercept. 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. Finally, perform the test of significance for the slope coefficient. ?(Show work)
Brand
Price
Score
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
Explanation / Answer
Regression equation is ,
Score = 8.8950+ 0.0138 Price
Slope = 0.0138 Slope is the change in the mean of distribution of Score by a unit change in Price.
Intercept =8.8950, this is the mean of the distribution of the Score when Price = 0
Coefficient of determination = 0.4908
Correlation coefficient = 0.701
The regression model can explain 49.08% variation in the dependent variable .
Estimate the overall score for a 42-inch plasma television ,
Score = 8.8950+ 0.0138 Price
price = 3800
Score = 8.8950+ 0.0138 *3800
Score = 55.82
test of significance for the slope coefficient,
pvalue(b1) = 0.024 < alpha = 0.05
Therefore reject H0.
SUMMARY OUTPUT Regression Statistics Multiple R 0.700603 R Square 0.490845 Adjusted R Square 0.4272 Standard Error 8.242984 Observations 10 ANOVA df SS MS F Significance F Regression 1 524.0257 524.0257 7.712294 0.024032 Residual 8 543.5743 67.94679 Total 9 1067.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 8.895044 14.95824 0.594658 0.568505 -25.5987 43.38881 -25.5987 43.38881 X Variable 1 0.013819 0.004976 2.777102 0.024032 0.002344 0.025294 0.002344 0.025294Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.