Please help with these SPSS questions!

Load the data set "Covid Deaths and Other Variables" into SPSS.

1. Reproduce the linear regression we saw earlier, in which the dependent variable was covid deaths per 1000 and the independent variable was doses per capita.

2. Some people have suggested that red states have had higher covid death rates because of imprudent political decisions and popular resistance to taking precautions. In SPSS, remove the doses per capita variable and replace it with the Trump share of the presidential vote in 2020.

(a) What is the coefficient on the Trump variable? State what it signifies in words. Does its t value suggest it is likely to be different from zero solely due to sampling variability?

(b) What is the adjusted R 2 of this regression equation? How does it compare to the adjusted R 2 of the equation you estimated in (1)?

3. Covid is much more dangerous to older people, and some states have a larger elderly share than others. Remove the Trump variable, and replace it with the over 65 share.

(a) What is the coefficient on the Over 65 variable? Its t value?

(b) What is the adjusted R 2 of this regression equation? How does it compare to the adjusted R 2 of the equation you estimated in (2)?

4. Now let's put all the variables together in a single equation. Continue to use the Covid death rate per 1000 as your dependent variable, but enter the other three variables as independent variables.

(a) Compare the three coefficients in this new model to the same coefficients when each independent variable was used separately (questions 1-3). Which have gone up and which have gone down? Are any of the new t statistics low enough to call the corresponding coefficient(s) into question?

(b) Compare the adjusted R 2 of this equation to the those of the previous equations. Which seems to better explain the variation in death rates?

5. To understand what is happening in the equation that uses all the variables, construct a correlation matrix. This is done by selecting Analyze/Correlate/Bivariate. Put all three of your independent variables in the correlation box.

(a) Are any of the variables strongly correlated? Define "strong" here as r > .5

(b) Why do you think this correlation exists?

6. Finally, run the regression again, this time using only doses per capita and over 65 as your independent variables. This time, also make "State" your source of case labels, and in the plot option make the dependent variable your Y variable and ZRESID your X variable.

(a) Has the adjusted R 2 gone up or down since removing the Trump variable? How does it compare to the adjusted R 2 in the equation with only doses per capita and the equation with only over 65?

(b) Are there any states that might be regarded as outliers on the basis of the residual plot? And did Oregon experience a higher or lower death rate than would have been expected based on the two explanatory variables in the regression?

(c) This is more demanding and optional: Considering the correlation matrix you created in (5), how would explain why over 65 seems to be a weak variable when considered alone (question 3) but serves a useful role when included with doses per capita, as in this part? If you can answer this correctly you will have taken a big step in model-building!

Link to SPSS "Covid Deaths and Other Variables" Data: https://docs.google.com/spreadsheets/d/1fNNANqwStyN3TfpRtA4VLQKLsMv5o4Bw/edit?usp=sharing&ouid=108170418555701779463&rtpof=true&sd=true

*[Anyone with the above link can access the excel file without needing to sign in]*