9. . Consumer Reports provided extensive testing and ratings for more than 100 H
ID: 3295164 • Letter: 9
Question
9. . 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 slightly changed here):
Brand
Price
Score
Dell
3500
60
Hisense
2800
55
Hitachi
3200
45
JVC
3500
50
LG
3300
55
Maxent
2000
30
Panasonic
4000
70
Phillips
3000
55
Proview
2500
35
Samsung
3000
40
Use the above data to develop an estimated regression equation and interpret results. Compute the Coefficient of Determination and the 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 $2900.
Brand
Price
Score
Dell
3500
60
Hisense
2800
55
Hitachi
3200
45
JVC
3500
50
LG
3300
55
Maxent
2000
30
Panasonic
4000
70
Phillips
3000
55
Proview
2500
35
Samsung
3000
40
Explanation / Answer
using minitab
Regression Analysis: score versus price
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 961.4 961.40 21.30 0.002
price 1 961.4 961.40 21.30 0.002
Error 8 361.1 45.14
Lack-of-Fit 6 198.6 33.10 0.41 0.834
Pure Error 2 162.5 81.25
Total 9 1322.5
Model Summary
S R-sq R-sq(adj) R-sq(pred)
6.71844 72.70% 69.28% 62.69%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -7.0 12.4 -0.56 0.588
price 0.01835 0.00398 4.62 0.002 1.00
Regression Equation
score = -7.0 + 0.01835 price
The regression line is
1)Y= -7.0 + 0.01835*x
2)The regression constant®ression coeff= -7.0& 0.01835
4)Since p-value =0.002<=0.05 So we reject the hypothesis
6)The coeff of determination isR^2 = 0.7270
The regression line is
1)Y= -7.0 + 0.01835*x
at x=2900
y=-7.0 + 0.01835*2900
score = 46.215
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