Question

id GPA Hours Work Video Texts Male Brown 1 2.99 3 0 5.5 50 0 1 2 3.25 25 0 0 300 0 0 3 3.20 11 24 0 30 0 0 4 3.20 14 0 16 40 1 1 6 3.20 20 0 0 150 1 1 7 2.04 3 8 40 1000 1 0 8 3.50 21 0 0 15 0 1 9 2.80 10 20 5 1500 0 1 10 3.82 100 0 0 0 0 1 11 3.79 14 4 10 1000 1 1 12 3.00 17.5 0 3 8 1 0 13 3.40 12 0 5 500 0 0 15 3.30 8 22 0 700 0 1 16 2.90 9 30 2 500 1 0 17 2.70 6 36 10 500 0 1 18 3.60 10 4 10 5 1 1 19 2.80 12 0 0 5 0 0 20 3.58 22 0 0 1 0 0 21 2.01 12 0 30 1500 1 0 22 3.20 21 25 3 300 1 1 24 3.30 2 20 5 5 1 0 25 2.75 5 25 3 1000 0 1 26 2.57 17.5 15 10 200 0 1 27 3.10 14 0 4 100 0 0 29 3.00 2 25 10 200 1 1 30 3.47 4 0 0 500 0 1 31 3.63 8 0 0 100 0 1 32 3.02 15 0 7.5 850 1 1 33 3.00 10 8 4.5 40 1 0 34 3.32 9 0 0 25 0 1 35 3.70 12 6 2 0 0 0 36 2.90 3 20 0 50 0 1 37 2.57 6 6 3 1000 1 1 38 1.96 3 30 10 1200 0 0 39 2.43 5 10 5 850 0 1 40 3.27 8 0 2 200 0 1 41 2.89 6 0 4 100 0 1 42 3.29 10 15 2 300 0 0 43 2.90 6 20 0 250 0 0 44 2.99 7 20 4 100 0 0 45 2.33 3 20 14 1100 1 1 46 3.82 18 0 0 50 0 0 47 3.40 8 20 0 200 1 1 48 2.28 2 20 18 950 1 0 49 3.68 8 5 3 250 1 1 50 2.92 3.5 10 3 200 1 1 51 3.31 7 10 4 50 0 1 52 3.98 30 0 0 50 0 0 53 3.82 40 5 2 100 0 0 54 2.85 7 10 2 500 0 1 55 2.95 6 20 0 100 1 1 56 3.78 12 10 0 50 1 0 57 2.63 6 40 5 700 1 1 58 2.63 6.5 10 7 600 1 0 59 3.18 5 10 5 500 1 1 60 3.45 14 10 3 100 0 0 61 3.58 9 0 2 100 0 1 62 2.84 4 20 2 600 1 0 63 2.70 4.5 20 6 800 0 1 64 2.93 8 10 3 50 1 1 65 3.29 9 0 0 100 0 1 66 2.95 4.5 0 0 200 0 0 67 3.13 6 10 0 50 1 0 68 2.54 7 0 3.5 900 0 0 69 2.88 9 10 0 550 0 1 70 2.41 4.5 15 10 1000 1 1

Q2. Suppose you are investigating the factors that affect college GPA. You perform a survey, and the data are contained in the Excel data file GPA_Survey.xlsx and then regress GPA on hours studied, work, video game, texts, and male.

1) Suppose you think that you have omitted an important variable, ability, which is correlated with many of your independent variables. What are the consequences of this omission on the coefficient estimates and hypothesis tests?

2) Perform the same regression that you did in part 1), but then add the additional variable, eye color. What are the consequences of including this irrelevant variable on your coefficient estimates and hypothesis tests?

3) Would you rather omit a relevant variable such as ability or include an irrelevant variable such as eye color? Explain your reasoning.

Answer 1

1) The results of the regression is:

If we omit an important variable, in this case, ability, then our R-squared decreases since we are leaving out the variation in the model.

Also, more importantly we have in our error term a factor like ability which is correlated with our independent variable. Thus, the assumption of orthogonality breaks down. The coefficient estimates are not likely to be a true estimates since error term is correlated with our independent variable.

2) After adding eye color, the regression output is:

THe consequence of adding an irrelevant variable doesn't change the value of coefficient estimate and p-value of our hypothesis tests.

3) We should avoid both but omiting the relevant variable is more damaging to the model since it leads to violation of orthogonality assumption making our OLS estimator a biased and not necessarily a best one in terms of variance.