Estimate the relationship between GPA and ACT using OLS; that is obtain the intercept and slope estimates in the equation (4 points) GPA 0 1ACT ˆ ˆ ˆ = + (c) Interpret the intercept ( 0 ˆ ) clearly (4 points). (d) Interpret the slope estimate ( 1 ˆ ) clearly (4 points).
Added by Zachary B.
Step 1
The model is: \[ GPA_i = \beta_0 + \beta_1 \times ACT_i + u_i \] Show more…
Show all steps
Your feedback will help us improve your experience
Syed Vasi and 51 other Microeconomics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 3.2 25 2 3.5 28 3 3.8 30 4 3.1 24 5 3.6 27 6 3.9 31 7 3.3 26 8 3.7 29 Estimate the relationship between GPA and ACT using OLS: that is, obtain the intercept and slope estimates in the equation GPA = β0 + β1 * ACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score increased by five points? (ii) Compute the fitted values and residuals for each observation and verify that the residuals (approximately) sum to zero. (iii) What is the predicted value of GPA when ACT = 20? How much of the variation in GPA for these eight students is explained by ACT? Explain:
Dominador T.
The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 i. Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPA = ̣̂β₀ + ̣̂β₁ ACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? ii. Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. iii. What is the predicted value of GPA when ACT = 20? iv. How much of the variation in GPA for these eight students is explained by ACT? Explain.
Madhur L.
The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPA = B0 + B1 * ACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? Compute the fitted values and residuals for each observation, and verify that the residuals are (approximately) zero. What is the predicted value of GPA when ACT = 20? How much of the variation in GPA for these eight students is explained by ACT? Explain.
Sri K.
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
Watch the video solution with this free unlock.
EMAIL
PASSWORD