Hi All
For Q15, they said for the answer: 'The midpoint, or predicted value is 0.0023 + 1.1163 x 0.05 = 0.058’
Question: why did they use 1.1163? I would have used 0.022 (standard error/ beta for regression analysis).
Any detailed explanation would be great.
Cheers
Have you noticed they are asking you the standard error of forecast of the dependent variable and not the common standard error of a slope, right?. Therefore, you must calculate the expected value of the dependent variable using the regression equation you are given (also called midpoint of a confidence interval, remember a CI is symmetrical):
exVIGRX = b0 + b1(exS&P500)
exVIGRX = 0.0023 + 1.1163 * 0.05 = 0.058 …note that 0.05 is the 5% value for exS&P500, so use it as input.
The other way to arrive at that 0.058 is using the CI you are provided in the question. A CI uses an expected value to create the range of values the true value of the variable would lie. So the mid point (the expected value of regression, because you are given the CI for the dependent variable) would just be (0.039 + 0.077) / 2 = 0.058. Using the regression equation would give you a more exact number though because this CI numbers are truncated to 3 decimals.
Now solve for the question.
The standard error of forecast is calculated using a weird formula (LOS 9.i at Schweser 2016), so is very unlikely you were asked to calculate it on the real exam. It will be directly an input like in this question.
Standard error of forecast is used to calculate the CI for the DEPENDENT VARIABLE, so:
CI(lower): 0.058 - 2.03 * Sf = 0.039
CI(upper): 0.058 + 2.03 * Sf = 0.077
Using any of those must give you the right answer 0.0093.
Hope this helps!