Wanda Brunner, CFA, is trying to calculate a 99% confidence interval for a regression equation based on the following information: Coefficient Standard Error Intercept -10.60% 1.357 DR 0.52 0.023 CS 0.32 0.025 What are the lower and upper bounds for variable CS? I am not sure how to come up with the confidence interval without knowing the number of observations
you do not need number of observations here. Confidence interval for CS = 0.32 +/- 3*(0.025) to clarify -> 0.32 = Value of Coefficient. 3 = Z-Value / T-Value for the 99% Confidence interval 0.025 = Std Error of CS variable.
Where did you get 3 as the critical t-value? Schweser’s answer says: The critical t-value is 2.42 at the 99% confidence level (two tailed test). The estimated slope coefficient is 0.32 and the standard error is 0.025. The 99% confidence interval is 0.32 ± (2.42)(0.025) = 0.32 ± (0.061) = 0.260 to 0.381. I am not sure how they arrived at 2.42 without knowing the number of observations?
sth strange with the text. Yes, you need to have n to calculate the critical value, if you don’t know the real stddev. Besides, the value given in the answer 2.42 cannot be correct under any circumstances for two-tailed, 99% confidence level, since z = 2.576 for standard normal distribution, two tailed 99% (and for t distr with n= infinity), so the right number has to be even higher than 2.576. Remember: you cannot have critical value < corresponding z number since t-distribution is a more ‘relaxed’ distribution than the standard normal distribution, with a fatter and less steep distribution graph. T-distribution is used for critical value where you don’t know the real distribution/standard deviation --> need to have a wider confidence band/range than the confidence band (of standard distribution) when you know the true standard deviation to compensate for the uncertainty.
2.58 is the actual z value for a 2-tailed. 3, I have seen used in some cases on CFAI mocks - where they talk of the nearest answer.
The T approximates the Z the higher the number of observations. So, 2.42 cannot be correct.