Question 13

Open R Studio and paste the following codes into a new R Script:

library(wooldridge) library(tidyverse) data(econmath,package="wooldridge") as_tibble(econmath)

The above will put a dataset, called econmath, into a tibble. This dataset, as the above codes suggest, comes from the wooldridge package in R. You cannot put this dataset into a tibble unless you call tidyverse package.

We are interested in estimating the parameters of the population regression function below:

score=a+b₁*acteng+b₂*actmth+b₃*colgpa+error

where variable score is the final grade in an upper elective undergraduate course (called: Mathematical Economics), acteng is the English ACT score, actmth is the Math ACT score, and colgpa is the GPA prior to taking this course. It should be noted that none of the above variables are put into log; there is no need for you to transform them either.

What is the point estimate for parameter b₁? (Note: your answer should be rounded up to only 2 decimal points).

answer____

Question 14

Consider the information in Question No. 13. What is the standard error associated with the point estimate for parameter b₁? (Note: your answer should be rounded up to only 2 decimal points).

answer_____

Question 15

Considering your answers to Questions No. 13 and 14, one can say that English ACT score:

Group of answer choices

is a significant determinant of the final grade in that college-level course. The t-value is quite low and the p-value is quite high.

is not a significant determinant of the final grade in that college-level course. The t-value is quite low and the p-value is quite high.

is not a significant determinant of the final grade in that college-level course. The t-value is quite high and the p-value is quite low.

is a significant determinant of the final grade in that college-level course. The t-value is quite high and the p-value is quite low.

Question 16

Consider the information in Question No. 13. Then, choose the correct statement below:

Group of answer choices (chose)

a. Unlike English ACT score, Math ACT score is not a significant determinant of the final grade.

b. Similar to English ACT score, Math ACT score is not a significant determinant of the final grade.

c. Similar to English ACT score, Math ACT score is a significant determinant of the final grade.

d. Unlike English ACT score, Math ACT score is a significant determinant of the final grade.

Question 17

Consider the information in Question No. 13. Also, consider the point estimate and the standard error for parameter b₃.

Suppose we pick up two hypothetical students from the population: Alex and Brit. At the beginning of the semester Alex's college GPA is one point greater than Brit's college GPA. Considering the 95% confidence interval estimation for parameter b₃,we expect Alex's final grade in this course to be between _______ and _______ points greater than Brit's final grade. (Note: your answer should be rounded up to only 2 decimal points).

Group of answer choices (chose)

a. 10.52; 14.21

b. 10.96; 13.77

c. 11.33; 13.40

d. 11.19; 13.54

Question 18

Consider the information in Question No. 13. What is the Multiple R-squared? (Note: your answer should be rounded up to only 2 decimal points).

answer______

Question 19

Consider your answer to Question No. 18. The obtained R-squared is a function of the coefficient of correlation between:

Group of answer choices (chose)

a. the obtained standard error.

b. observed and modeled college GPAs.

c. observed and modeled final grades.

d. the obtained estimated parameter.

Question 20

Reflect upon your answer to Question No. 19. Comparing models with identical number of independent variables, the higher the R-squared,:

Group of answer choices (chose)

a. the worse the linear fit of the model.

b. the higher the p-values.

c. the lower the t-values.

d. the better the linear fit of the model.