Regression Analysis

QBAAssignmentAutumn2019questions2.docx

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Question D (12 marks) – QBA Class Survey

Introduction

Each semester for the last 2 years we have been collecting data (in class) from QBA students about their performance on Quiz 1, the number of hours they studied each week, and a number of other variables that potentially could explain their quiz performance (such as whether they go to U:PASS etc.)

The students self-reported all answers and the data has also been cleaned for outliers. The variables included in the dataset correspond to the answers for each question on the survey and a description of each data series is given below:

Series in Dataset:

ActScore: Score on Quiz 1 reported by the student (out of 15)

ExpScore: Score on Quiz 1 that the student expected to achieve (out of 15)

nHrs: Number of hours the student reported to study for QBA each week

Age: Student’s age (in years)

Height: Student’s height (in centimeters)

BigBang: Rating (on a scale of 0 to 10; 10 being the highest) of how much the student enjoys ‘The Big Bang Theory’ television show

Female: Student’s gender (1 = female, 0 = male)

MathBack: If the student reported to have a strong math background (1 = yes, 0 = no)

UPASS: If the student reported to attend U:PASS sessions (1 = yes, 0 = no)

Aussie: If the student completed their high school in Australia (1 = yes, 0 = no)

LikeMath: If the student reported to like mathematics (1 = yes, 0 = no)

Kris: If the student was in a semester when Kris lectured (1 is Kris was the teacher and 0 otherwise)

Use the data in Assignment Data.xlsx, tab: QBA Survey Results to answer the following questions:

A1. (2 marks) Run a regression of actual test scores (ActScore) on the number of hours studied per week (nHrs). Report the regression output. What is the estimated effect of nHrs on test scores? Is this relationship statistically significant? If a student increased the number of hours studied per week from 3 to 10, how are test scores expected to change?

A2. (1.5 mark) Run a regression of ActScore on nHrs and include the following control variables: Age, Female, Aussie, Mathback, and UPASS. Report the regression output. Are the results from this regression substantively different from the results in A1 regarding the effect of nHrs on ActScore? What bias does the regression in A1 appear to suffer from?

A3. (0.5 mark) Janet is 24-year-old QBA student who completed high school in Australia and considers herself to have a strong mathematical background. If she studies 6 hours a week but does not attend U:PASS session what is Janet’s predicted test score based on the regression in A2?

A4. (1.5 marks) Are gender and age determinants of test scores? Test the null hypothesis that Female can be deleted from the regression (in A2). Test the null hypothesis that Age can be deleted from the regression. Test the null hypothesis that both Female and Age can be deleted. Be sure to state the null and alternative hypothesis in each case the value of the relevant test statistic and its critical value used to perform the test.

A5. (1 mark) Answer the following questions by running (and reporting the output of) regressions with only one independent regressor: (i) Does the lecturer of the subject make a statistically significant difference to test scores? (ii) Is there any statistical evidence that males are more confident in their abilities than females?