The R program F_t_significance generates three standard normal independent variables (V1, V2, V3), an error term (U), and sets the dependent variable (Y) to

Y = 1 + U

It the runs the regression of y on V1, V2, V3 and computes the p-values of the individual tests

- Run this program 20 times (you can either manually run it twenty times or put the program in a loop and run it once).(a) Produce a table with 20 rows. Each row of the table contains the three p-values of the t-statistics for the slope coefficients and the p-value of the F-statistic for the overall regression.(b) How many times did you reject the zero null hypothesis, at the 10% level, for the 60 t-statistics? How many times would you expect to reject the zero null hypothesis at the 10% level?(c) How many times did you reject the zero null hypothesis, at the 10% level, for the 20 F-statistics? How many times would you expect to reject the zero null hypothesis at the 10% level?
- Change the program so that there are ten independent variables as opposed to three. Run this program 20 times (you can either manually run it twenty times or put the program in a loop and run it once).(a) Produce a table with 20 rows. Each row of the table contains the ten p-values of the t-statistics for the slope coefficients and the p-value of the F-statistic for the overall regression.(b) How many times did you reject the zero null hypothesis, at the 10% level, for the 100 t-statistics? How many times would you expect to reject the zero null hypothesis at the 10% level?(c) How many times did you reject the zero null hypothesis, at the 10% level, for the 20 F-statistics? How many times would you expect to reject the zero null hypothesis at the 10% level?
- In how many of the 40 cases above, did you reject the zero null for the F-test, but did not reject the zero null for any of the individual t-tests?
- In how many of the 40 cases above, did you not reject the zero null for the F-test, but did reject the zero null for at least one of the individual t-tests?

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