Question 1:

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).

Question 2:

Consider the information in Question No. 1. 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).

Question 3:

Considering your answers to Questions No. 1 and 2, one can say that English ACT score:

Group of answer choices

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.

a. 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.

b. 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.

c. 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.

Question 4:

Consider the information in Question 1. Then, choose the correct statement below:

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

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

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

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

Question 5:

Consider the information in Question 1. 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. (Your answer should be rounded up to only 2 decimal points).

Choose the correct answer:

a. 11.19; 13.54

b. 11.33; 13.40

c. 10.52; 14.21

d. 10.96; 13.77

Question 6:

Consider the information in Question number 1. What is the Multiple R-squared? (Your answer should be rounded up to only 2 decimal points).

Question 7:

Consider your answer to Question number 6. The obtained R-squared is a function of the coefficient of correlation between:

Choose the correct answer:

a. observed and modeled college GPAs.

b. the obtained standard error.

c. observed and modeled final grades.

d. the obtained estimated parameter.

Question 8:

Reflect upon your answer to Question number 7. Comparing models with identical number of independent variables, the higher the R-squared:

Choose the correct answer:

a. the worse the linear fit of the model.

b. the higher the p-values.

c. the better the linear fit of the model.

d. the lower the t-values.