Question

Researchers try to predict students' SAT scores from their ACT (American College Testing) scores. The regression equation to be estimated in this research is: y = a + bx where y is the SAT score and x is the ACT score. The researchers collected data from 60 freshmen who had taken both exams. Use the attached dataset to estimate the above regression equation in Excel. Use the regression results to answer the following 10 questions (1)-(10). The data "Scores" is attached. Scores.xlsx What is the independent variable and what is the dependent variable in this research? (2 points) Based on the regression results, estimate the slope b and the y-intercept a in the regression equation y = a + bx. (2 points) Find the correlation coefficient r between x and y. (2 points) Report the coefficient for x (the slope) with its standard error. (2 points) Construct the test for the hypothesis H0: b = 0. Give the t-stat and p-value. (2 points) Is the coefficient for ACT significant at α = 0.10 significant level? (2 points) Can you reject the null hypothesis H0: b = 0? (2 points) Interpret the meaning of the coefficient. Is the ACT score a strong influence on the SAT score? (2 points) Identify R2 from the regression results. Explain the meaning of R2. (2 points) Sandy is a freshman who took the ACT exam. Her score was 23. How do you predict her SAT score based on the regression result? (2 points)

          Researchers try to predict students' SAT scores from their ACT (American College Testing) scores. The regression equation to be estimated in this research is:
y = a + bx
where y is the SAT score and x is the ACT score. The researchers collected data from 60 freshmen who had taken both exams. Use the attached dataset to estimate the above regression equation in Excel. Use the regression results to answer the following 10 questions (1)-(10).

The data "Scores" is attached. Scores.xlsx

What is the independent variable and what is the dependent variable in this research? (2 points)

Based on the regression results, estimate the slope b and the y-intercept a in the regression equation y = a + bx. (2 points)

Find the correlation coefficient r between x and y. (2 points)

Report the coefficient for x (the slope) with its standard error. (2 points)

Construct the test for the hypothesis H0: b = 0. Give the t-stat and p-value. (2 points)

Is the coefficient for ACT significant at α = 0.10 significant level? (2 points)

Can you reject the null hypothesis H0: b = 0? (2 points)

Interpret the meaning of the coefficient. Is the ACT score a strong influence on the SAT score? (2 points)

Identify R2 from the regression results.

Explain the meaning of R2. (2 points)

Sandy is a freshman who took the ACT exam. Her score was 23. How do you predict her SAT score based on the regression result? (2 points)

Added by Esperanza P.

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