You want to estimate the relationship between students' score (Score) in a course and the number

Step 1: Recall the formula for the OLS estimator of the slope (β1) in a simple linear regression

Question

You want to estimate the relationship between students' score (Score) in a course and the number of times they ask question to instructor of the course (Q): Score$_i = \beta_0 + \beta_1 Q_i + u_i$ where $\beta_0$ is the intercept of the population regression line; $\beta_1$ is the slope of the population regression line; $u_i$ is the error term; and the subscript $i$ runs over observations, $i = 1, \dots, n$. You collect data from a random sample of 300 students. After analyzing the data, you determine that the covariance between students' score and the number of times they ask question to instructor is 4.85 and the variance of the number of times they ask question to the instructor is 3.59. You also find that the mean score of students in the sample is 63.82 and the mean number of times they ask question to the instructor is 2.75. The OLS estimator of the slope $\beta_1$ is (Round your answer to two decimal places.) The OLS estimator of the intercept $\beta_0$ is (Round your answer to two decimal places.) Which of the following statements are true in describing the estimates of the coefficients of the regression line? (Check all that apply.) A. The slope, $\beta_1$, is the students' score due to a unit change in the number of times they ask question to instructor. B. You do not have enough information to tell whether the correlation between students' score and the number of times they ask question to instructor is positive or negative. C. The slope, $\beta_1$, is the change in students' score due to a unit change in the number of times they ask question to instructor. D. The correlation between students' score and the number of times they ask question to instructor is positive.

You want to estimate the relationship between students' score (Score) in a course and the number of times they ask question to instructor of the course (Q):
Score$_i = \beta_0 + \beta_1 Q_i + u_i$
where $\beta_0$ is the intercept of the population regression line; $\beta_1$ is the slope of the population regression line; $u_i$ is the error term; and the subscript $i$ runs over observations, $i = 1, \dots, n$.
You collect data from a random sample of 300 students. After analyzing the data, you determine that the covariance between students' score and the number of times they ask
question to instructor is 4.85 and the variance of the number of times they ask question to the instructor is 3.59. You also find that the mean score of students in the sample is 63.82
and the mean number of times they ask question to the instructor is 2.75.
The OLS estimator of the slope $\beta_1$ is
(Round your answer to two decimal places.)
The OLS estimator of the intercept $\beta_0$ is
(Round your answer to two decimal places.)
Which of the following statements are true in describing the estimates of the coefficients of the regression line? (Check all that apply.)
A. The slope, $\beta_1$, is the students' score due to a unit change in the number of times they ask question to instructor.
B. You do not have enough information to tell whether the correlation between students' score and the number of times they ask question to instructor is positive or negative.
C. The slope, $\beta_1$, is the change in students' score due to a unit change in the number of times they ask question to instructor.
D. The correlation between students' score and the number of times they ask question to instructor is positive.

Added by Megan A.

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