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


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!

 

[mighty2000]

I would like to offer some clarification and additional information to the points you have raised.

Firstly, the equation provided is a least squares regression model, which means that it is used to estimate the relationship between the dependent variable (Y) and the independent variables (A-D) based on the given sample data. The coefficients (0.954, 0.134, 0.255, and 0.052) represent the estimated effect of each independent variable on the dependent variable, and the standard errors (0.32, 0.117, 0.043, 0.019, and 0.006) represent the uncertainty in these estimates. The R^2 value (0.581) indicates the proportion of variation in the dependent variable that can be explained by the independent variables.

Now, moving on to your questions:

A. Testing the null hypothesis that the coefficient on D is equal to 0 means that we are testing whether there is a significant relationship between D and Y. In this case, we can use the t-test to determine the p-value, which is the probability of obtaining a coefficient of 0.052 or higher if the true coefficient is actually 0. If this p-value is less than the chosen significance level (usually 0.05), we can reject the null hypothesis and conclude that there is a significant relationship between D and Y.

B. To construct a 95% confidence interval for the coefficient on D, we can use the formula you have provided. This interval represents the range of values within which the true population regression coefficient on D is likely to fall with 95% confidence.

C. As you have correctly stated, the probability that this interval contains the true population regression coefficient on D is 95%.

I hope this helps clarify the concepts and calculations involved in this problem. Let me know if you have any further questions.