Run the appropriate regression to test

Question

Assignment Task: An unnamed college administration is interested in the effect of study hours on GPA. Data are available for an i.i.d. random sample of students. There is a copy of this data in the file DropBox/105 (Statistics) class space/exam2l/exam2,_data.xlsx. GPA is a student's grade point average in GPA points. Study Hours is measured in hours studied last week. Male is a dummy variable equal to 1 if male, 0 if female (only 2 genders are represented in this dataset). Right is a dummy variable equal to 1 if the student is right-handed. Loft is a dummy variable equal to 1 if the student is left-handed. Assume that if a person is not Right-handed or Left-handed, they are Ambidextrous. That is, Right means "only right-handed" and Left means "only left-handed."

Question 1: Consider the following model: GPA_i = β₀ + β₁StudyHours_i + β₂Male_i + ε_i

Do males have lower GPAs on average, than females, at the 5% significance level, controlling for study hours?

Run the appropriate regression to test this and calculate the relevant statistics to support your answer.

Question 2: Does the effect of study hours on GPA differ by gender?

Run the appropriate regression to test this and calculate the relevant statistics to support your answer.

Question 3: Consider the "handedness" variables now. At what significance level can you conclude that Right-handed students have higher GPAs than Left-handed students (controlling for study hours and gender)? Estimate the appropriate regression and calculate the relevant statistics to support your answer.

Question 4: Consider the following model

GPA_i = β₀ + β₁ StudyHours_i + β₂Male_i + β₃Right, + β₄Left,+ β₆StudyHours_i2; + ε_i.

Estimate this model, write down the sample regression function, and interpret the coefficient on Right

Question 5:  For the model in part (d), at the 5% level, test whether study hours is a significant determinant of GPA. Write down the null and alternative hypotheses.

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