Use the dataset attached to this homework in MS Excel format. Use Gretl. The data shows the number of minutes it took students to submit homework and corresponding grades earned (from an Econ 205 Principles of Macroeconomics). Students were allowed to submit homework without time restrictions: they could start and finish at any time. The question of interest is to determine if there is a correlation between the time taken to submit homework and the grade earned. Ex ante I can think of reasons why submission times may be correlated to grades: low minutes indicates giving up or starting homework too late and running out of time; taking too long indicates that students are trying to study as they submit homework, not a good strategy. Run a linear regression model using minutes as the independent variable and grades as the dependent variable. In homework 6 I asked you to work with the data as provided. Now, I will ask you to replicate by work as presented in class. 1. Work on a subsample that only includes time <60minutes. Why am I doing it? (20 points) 2. Print the summary statistics and graph minutes and grades. What are the main differences between the result from the sub sample and the whole? (20 points) 3. Run an OLS on the data. Use grade as the dependent variable and minutes as the independent variable. a. Print the result. Note anything you can infer from the result. (20 points) b. Graph residuals (scatter plot against x). Note anything you can infer from the graph--which assumptions of the linear regression model can be visually tested? (20 points) c. Save the residuals and fitted regression in Gretl dataset. (20 points) d. Find summary statistics of residuals. Note anything you can infer from the graph--which assumptions of the linear regression model can be assessed? (20 points) 1 e. Graph the histogram (frequency using Gretl nomenclature) of the residuals. What can you say about the assumption of normality? (20 points) f. What can you conclude about these results and my original hypothesis? (40 points) 4. It is more appealing to work with logarithms because the estimates are elasticities (the percent change of time over the percent change of grade). Create the logarithm of minutes and grade, and then run an OLS model with log(grade) as the dependent variable and log(minutes) as the independent variable. A 1% change in minutes is related to x% change in grade. What is x? (40 points)
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