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For the following THREE (3) questions assume the following scenario and use the below output Before the experiment; the researcher specified six specific comparison...

Question

For the following THREE (3) questions assume the following scenario and use the below output Before the experiment; the researcher specified six specific comparisons of theoretical interest: The output for those six comparisons is provided below: Contrast Coefficients strain of rat mixed Contrast bright dull Contrast Tests Value of Contrast Std Error 6250 1.2611 2.5000 1.2611 3.5625 1.0921 ~3750 2.1842 -3.3750 1.0921 2.1250 12611 -4.6250 1.2825 2.5000 1.1319 3.5625 1.0009 ~3750 2.1465 3.3750 1.1

For the following THREE (3) questions assume the following scenario and use the below output Before the experiment; the researcher specified six specific comparisons of theoretical interest: The output for those six comparisons is provided below: Contrast Coefficients strain of rat mixed Contrast bright dull Contrast Tests Value of Contrast Std Error 6250 1.2611 2.5000 1.2611 3.5625 1.0921 ~3750 2.1842 -3.3750 1.0921 2.1250 12611 -4.6250 1.2825 2.5000 1.1319 3.5625 1.0009 ~3750 2.1465 3.3750 1.1935 2.1250 13582 Contrast Assume equal varances Sig_(2-tailed 001 054 002 864 003 099 001 035 001 862 009 129 learning core 3.668 1.982 -3262 ~172 -3.090 -1685 3.606 -2209 3.559 ~175 2.828 1565 Does not assume equal vanances 26.848 29.286 37.379 30.950 23.934 28.879



Answers

$$
\begin{array}{l}{\text { Use the data in CATHOLIC to answer this question. }} \\ {\text { (i) In the entire sample, what percentage of the students attend a Catholic high school? What is the }} \\ {\text { average of math12 in the entire sample? }} \\ {\text { (ii) Run a simple regression of math } 12 \text { on cathhs and report the results in the usual way. Interpret }} \\ {\text { what you have found. }}\end{array}
$$
$$
\begin{array}{l}{\text { (iii) Now add the variables lfaminc, motheduc, and fatheduc to the regression from part (ii). How }} \\ {\text { many observations are used in the regression? What happens to the coefficient on cathhs, along }} \\ {\text { with its statistical significance? }}\end{array}
$$
$$
\begin{array}{l}{\text { (iv) Return to the simple regression of } m a t h 12 \text { on cathis, but restrict the regression to observations }} \\ {\text { used in the multiple regression from part (ii). Do any important conclusions change? }}\end{array}
$$
$$
\begin{array}{l}{\text { (v) To the multiple regression in part (iii), add interactions between cathhs and each of the other }} \\ {\text { explanatory variables. Are the interaction terms individually or jointly significant? }}\end{array}
$$
$$
\begin{array}{l}{\text { (vi) What happens to the coefficient on cathhs in the regression from part (v). Explain why this }} \\ {\text { coefficient is not very interesting. }} \\ {\text { (vii) Compute the average partial effect of cathhs in the model estimated in part (v). How does it }} \\ {\text { compare with the coefficients on cathhs in parts (iii) and (v)? }}\end{array}
$$


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