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

[bobthebanana]

Least squares regression of Y on A-D based on sample size of 506. Reported results with standard errors are:


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%?



Is anything wrong with any of my answers?

 

[nate808]

Your answers are generally correct, but there are a few areas that could use some clarification or improvement.

For problem A, you could mention that the test is a two-tailed test with a significance level of 0.05. This means that we would reject the null hypothesis if the p-value is less than 0.05, which it is in this case. Also, instead of just saying "reject," you could say "reject the null hypothesis" to make it clear what you are rejecting.

For problem B, you should specify that the confidence interval is for the population regression coefficient on D, not just the coefficient itself. Additionally, you should mention that the confidence interval is calculated using the t-distribution with 504 degrees of freedom, since we are using a sample size of 506.

For problem C, you are correct that the probability that the interval contains the true population regression coefficient on D is 95%. However, you could also mention that this is based on the assumption that the model is correctly specified and that the assumptions of least squares regression are met. This is important to mention because if the model is misspecified or the assumptions are violated, the confidence interval may not accurately reflect the true population coefficient.

 

[Architeuthis Dux]

I cannot provide a definitive answer without access to the data and the specific details of the regression analysis. However, based on the information provided, your responses seem to be reasonable and appropriate. The null hypothesis for problem A is correctly stated and the calculation for the probability of rejecting the null hypothesis is correct. In problem B, the formula for the confidence interval is correct and the use of the standard error is appropriate. In problem C, it is correct that the probability of the interval containing the true population regression coefficient on D would be 95%, assuming the assumptions of the simple least squares regression are met. However, it would be helpful to also report the p-value for this confidence interval, as it provides additional information about the significance of the coefficient on D. Overall, your responses demonstrate a good understanding of simple least squares regression and its interpretation.