## (Solution document) Consider the multiple regression model, E(y) = 0 + 1x1 + 2x2 + 3x3 , where y = exam score (ranging from 0 to 100 points), x1 = amount paid to a tutor...

1. Consider the multiple regression model,  E(y) = ?0 + ?1x1 + ?2x2 + ?3x3 ,  where y = exam score (ranging from 0 to 100 points), x1 = amount paid to a tutor (dollars), x2 = number of hours of sleep per week,            and  x3 = number of hours of study time.  How many independent variables are included in the model?

A. 4

B. 1

C. 3

D. 2

2.The multiple regression model, E(y) = ?0 + ?1x1 + ?2x2 + ?3x3  ,  where y = exam score (ranging from 0 to 100 points), x1 = amount paid to a tutor (dollars), x2 = number of hours playing video games per week,       x3 = number of hours of study time, yielded the following prediction equation:

y-hat = 65 + .2x1 - 1.5x2 + .5x3

A practical interpretation of the estimated beta for x2 is "exam score decreases 1.5 points for every 1 hour increase in playing video games..." What statement needs to be added to the end of the interpretation to make it valid?

A. ... holding x1 = amount paid to a tutor and x3 = number of hours of study time fixed (or constant)

B. ... holding x2 = number of hours playing video games per week fixed (constant)

C. ... when x1 = amount paid to a tutor = \$0 and x3 = number of hours of study time = 0 hours

D. ... with 95% confidence

3.In the multiple regression model, E(y) = ?0 + ?1x1 + ?2x2 + ?3x3,  the null hypothesis of interest for the global F-test is:

Ho: ? 1 = ? 2 = ? 3 = 0

A.True

B.False

4.The multiple regression model, E(y) = ?0 + ?1x1 + ?2x2 + ?3x3 , where y = exam score (ranging from 0 to 100 points), x1 = amount paid to a tutor (dollars), x2 = number of hours playing video games per week, and x3 = number of hours of study time, yielded R2 = .65. Give a practical interpretation for this statistic.

A.65% of the time the multiple regression model will be a good predictor of exam score

B.We are 65% confident that the multiple regression model is a statistically useful predictor of exam score

C.65% of the exam scores are not equal to their predicted values

D.65% of the sample variation in exam scores can be explained by the multiple regression model

5.The value of R2 for the multiple regression model, E(y) = ?0 + ?1x1 + ?2x2 + ?3x3 , will be larger than the value of R2 for the simple linear regression model, E(y) = ?0 + ?1x1

A.True

B.False

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