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

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The discussion centers on a least squares regression analysis of Y on variables A-D, utilizing a sample size of 506. The regression equation is Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D, with an R² value of 0.581. Key problems addressed include testing the null hypothesis for the coefficient on D, constructing a 95% confidence interval for D, and evaluating the probability that this interval contains the true population regression coefficient. The analysis reveals that the standard deviation of D should not be divided by the square root of the sample size when calculating the confidence interval.

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bobthebanana
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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%?


___________

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!
 
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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.