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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&regression 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