# Simple least squares regression problem. Am I doing anything wrongly?

Least squares regression of Y on A-D based on sample size of 506

Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D
s.errs (0.32) (0.117) (0.043) (0.019) (0.006)

R^2 = 0.581

problem A. Test null that coefficient on D is equal to 0
d = coefficient on D
null: D ~ N(0, 0.006)
Pr(d >= 0.052) = 1 - normalcdf(0.052 / 0.006) = 0
reject

problem B. Construct 95% confidence interval for coefficient on D
0.052 +/- 1.96*(0.006 / sqrt(506))

problem C. What is the probability that this interval contains the true population regression coefficient on D?
??? just 95%?

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The problem gives a lot of info and I only use very little of it, which leads me to believe I'm doing something wrongly. Am I?

Thanks for the help!

## Answers and Replies

Looks okay except in part B. The output of the regression is giving you the estimated standard deviation of D, so you don't have to divide by sqrt(506). If you wanted to nitpick you could use the t distribution instead of the normal distribution, but since you have 506 observations it is probably not an issue.