Question 4. You have estimated the following regression model Feeling Thermomete

Question

Question 4.

You have estimated the following regression model

Feeling Thermometer Rating of Obama = 44 + 25*Obama Approval + 12*Liberal + 2*race + controls

Where Obama Approval is a dummy variable coded 1 for approve and 0 for disapprove, and liberal is a dummy variable coded 1 for liberal and 0 otherwise. Race is coded 1 for white, 2 for black, and 3 for all other races. Obama approval is a statistically significant predictor, and liberal and race are not.

4a. Your r-squared for this model is .96. In a model excluding a control for Obama approval, your r-squared is only .32. Another researcher says you MUST use the first model, as it has a higher r-squared and is a better predictor. Do you agree? Explain why or why not (10 points)

4b. Do you believe the results of this model, that being liberal does not significantly impact support for Obama? Explain why using what you know about statistics (8 points)

4c. Another researcher says that, since you aren’t going to explain the control variables in the text of your article, you shouldn’t include them in the model. Explain why he is wrong (8 points).

4d. Race is not a statistically significant predictor in your model of support for Obama, but you are not convinced this is right. Explain a problem with how you included race in your model and how you can fix it (8 points).

4e. You add a control in your model for age. This is not a statistically significant predictor. What will happen to you r-squared? Explain how you know (6 points)

Explanation / Answer

A) It is given in the model that obama approval is a significant variable while other are not, we can reject the variables from the model which are not significant, but problem here is that obama approval is a binary variable i.e. 0 or 1.

that means if we remove the signicant variable and just keep insignificant variable, the model is not going to be a good model i.e. R square value is going to be low. But we should also see Adjusted R square value while removing the variables from the model.

Selection of variable or rejection of variable from the model should be based on the adjusted R square value. But yes we must use the model which have higher R square. So we should use the model whose R square is .95 until we dont see Adjusted R square value.

B) Without performaning correlation test we cannt say anything about support i.e. we cannt say that being liberal support obama approval. We should calculate correlation matrix of these independent variable to check this.

C) Not explaining control variable does not mean that control variable has no effect on our model hence whichever variable is useful and significant should be included in the model. Atleast the effect of this variable should be tested without concluding anything Hence we should take this into account and do the relevent test even if it is not explained in the article.

D) Although a variable may not be significant in the model but there may be an effect of this variable into another variable. Hence we should create one more dummy variable with this two variable and check the influence on the model. Correlation matrix is a powerful tool here to explain this.

E) Whenever we add a variable which is not significant for our model, it may decrease the R square or may not affect the R square, but yes if we add any insignificant variable into the model the adjusted R square value goes down.

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