b. Best Definition (Make sure to supplement your answers with the relevant graph): (5 points) Given the following univariate regression: Y₁ = ß₁ + Â₂ס + Û₁ Prove that ẞ2 is the best (15 points) 1. Define and mathematically prove the following statistical concepts a. Unbiased aluguend Definition (Make sure to supplement your answers with the relevant graph): ASOS aninge (5 points) эшви odmusbo Iwer bac garbanove oil glad con of complaisas svig antisa i Tari contis I scombueno que seu jod orabo gru Given the following univariate regression: Y₁ = Â₁ + Â₂ס + û₁ Prove that E(B2) = B₂ (10 points) Il mexa of 208

You are interested in how the number of hours a high school student has to work in an outside job has on their GPA. In your regression you want to control for high school standing and so you run the following regression: GPA = 3.4 0.03 * HrsWrk - 0.7 * Frosh - 0.3 * Soph +0.1 * Junior (1.1) (0.013) (0.23) (0.14) (0.08) where HrsWrk is the number of hours the student works per week, and Frosh, Soph, and Junior are dummy variables for the student's class standing. a) If you include a dummy variable for seniors, that would cause a Hint: type one word in each blank. For the rest of questions, type a number in one decimal place. b) The expected GPA of a Sophomore who works 10 hours per week is c) The expected GPA of a Senior who works 10 hours per week is d) If Dom and Sarah work the same number of hours per week, but Dom is a Junior and Sarah is a Freshman. Dom is expected to have a higher GPA than Sarah. e) Suppose you rewrite the regression as: problem. GPA = ₁HrsWrk + ß2Frosh + B2Soph +…

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