Question

8. Practice constructing confidence intervals Suppose a data set of 30 observations (N-30) was analyzed using OLS to examine the factors influencing the participation rate of employees in a 401(k) retirement plan sponsored by their employer. The regression results are as follows, with standard errors in parentheses: prate = 80.1 + 5.6mrate + 0.046 age + 0.0001 totemp 0.s5) (0.04) (S.OR-5) where prate - percentage of eligible workers with a 401(k) plan mrate match rate for firm age - age of the 401(k) plan totemp - total number of employees at the firm R2 0.521 degrees of freedom. Based on the number of observations and parameters in the model, there are to construct a 95% confidence interval around al. To do this, you would need c, the value of the the denrees of freedom). This confidence interval would be th percentile of Suppose you would like . (Hint: The relevant value c is equal

Answer 1

Based on the number of observations and parameters in the mode, there are 30 - 4 = 26 degrees of freedom.

Suppose you would like to conduct a 95% confidence interval around $\hat{\beta_1}$ , to do this, you would need c, the value of the 97.5 th percentile of the t distribution (given the degrees of freedom) . The confidence interval would be

$=(\hat{\beta_1} - t_{0.025,26}SE(\hat{\beta_1}), \hat{\beta_1} +t_{0.025,26}SE(\hat{\beta_1}))$

5.6 0.0816