BUAD 280 Southern California Statistics Multiple Regression Question

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Multiple Regression Assignment
Section I: Multiple Choice
Instructions: There may be anywhere from 0 to 5 correct answers for each question. Put an “X”
in front of each correct answer.
1) You are conducting a regression predicting college GPA from high school GPA. You
find a standardized regression coefficient of 0.30. This means:
____ a. The slope of the regression line of high school GPA in predicting college
GPA is positive.
____ b. The correlation between college GPA and high school GPA is 0.30.
____ c. High school GPA explains 9% of the variance in college GPA.
____ d. A one standard deviation increase in high school GPA is associated with a
0.30 standard deviation increase in college GPA.
____ e. A one-point increase in high school GPA (e.g., from 2.0 to 3.0) is
associated with a 0.30-point increase in college GPA (e.g., from 2.0 to
2.50).
2) After you run a bivariate regression of Y on X on a dataset with n=10,000, you see that
the t-statistic for your predictor X is 3.05. You have set your alpha to be 0.05 and you
know that the t-critical is 1.96 with this sample size and alpha level. What can you
conclude?
____ a. The regression coefficient for X is significantly different from 0.
____ b. The variable X explains 3.05% of the variance in Y
____ c. The p-value associated with the regression coefficient for X is less than
0.05.
____ d. We can be 95% confident that there is a non-zero relationship between X
and Y.
____ e. The 95% confidence interval will include zero.
3) The following diagram represents the proportion of the variance in Y that is explained by
X1 and X2 in a multiple regression analysis. Assuming that the area of each labeled
section is non-zero, you know that:
____ a. The R2 for the multiple regression of Y
on X1 and X2 is represented by a+b+c.
____ b. There is redundancy between X1 and X2
in predicting Y.
____ c. The R2 for the bivariate regression of Y
on X1 is represented by section a.
____ d. The squared semi-partial correlation of
Y and X2 controlling for X1 is
represented by section b.
____ e. The semi-partial correlation of Y and X1
controlling for X2 is ?