Can you help me for G) AND H)? :) g) Use the corr command to find the correlatio

Question

Can you help me for G) AND H)? :)

g) Use the corr command to find the correlation between tuit17 and tuit18. Explain why using the average tuition over two years might be preferred to adding both tuition variables to the model as separate explanatory variables. Create a variable for average tuition and re-estimate the model using this variable (but exclude tuit 17 and tuit18). What happens to the statistical significance of tuition when you use the average over two years h) Do the results for the average tuition variable make sense when interpreted causally? What might be going on?

Explanation / Answer

g) The new derived variable i.e. average of both tuitions will be still significant. Since at least one of the root variables was significant in the model and there is high correlation between both.

h) Yes, it can be interpreted as follows:

There will be an increase of beta (slope coefficient) with unit increase in the average of both the tuitions.

Since, data is not given, so worked out on a dummy data to prove this:

y x1 x2 x_ave SUMMARY OUTPUT SUMMARY OUTPUT 1 0 -1 -0.5 2 2 2 2 Regression Statistics Regression Statistics 7 6 5 5.5 Multiple R 0.972895 Multiple R 0.951951 8 9 10 9.5 R Square 0.946524 R Square 0.906211 2 2 2 2 Adjusted R Square 0.939394 Adjusted R Square 0.900349 4 5 6 5.5 Standard Error 0.726379 Standard Error 0.931423 6 5 6 5.5 Observations 18 Observations 18 1 0 0 0 8 7 6 6.5 ANOVA ANOVA 2 1 2 1.5 df SS MS F Significance F df SS MS F Significance F 9 10 10 10 Regression 2 140.0856 70.0428 132.7506 2.89E-10 Regression 1 134.1192 134.1192 154.5957 1.23E-09 3 4 4 4 Residual 15 7.914405 0.527627 Residual 16 13.88077 0.867548 3 2 2 2 Total 17 148 Total 17 148 5 5 4 4.5 3 3 2 2.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 3 4 5 4.5 Intercept 0.778313 0.278487 2.794796 0.013602 0.184733 1.371894 0.184733 1.371894 Intercept 0.846418 0.356153 2.37656 0.030298 0.091408 1.601428 10 11 10 10.5 x1 1.157727 0.222209 5.210074 0.000106 0.684099 1.631354 0.684099 1.631354 x_ave 0.831318 0.06686 12.43365 1.23E-09 0.68958 0.973055 1 0 0 0 x2 -0.31996 0.220304 -1.45235 0.167002 -0.78953 0.149609 -0.78953 0.149609

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