1. Circle the number which corresponds to the correct answer.

(a) Suppose you are in charge of forecasting natural gas prices for an energy company, a task for which you use a multiple regression. You must deliver your forecast for next week's price, with confidence level 95%. You need:

#1: a confidence interval for mean price given values of the independent variables.

#2: a prediction interval for an individual price given values of the independent variables.

(b) You run a regression of Y on five different independent variables. While the F test yields significant evidence that at least one independent variable in linearly related to Y, all the t tests for the individual independent variables have very high p values. This is because:

#1: the p values for the individual t tests have not been adjusted for the multiple comparison problem.

#2: the independent variables are most likely multicollinear.

2. Each of the statistical conclusions below has something wrong with it. Rewrite the underlined conclusion. Assume the test itself is correctly reported, it is the conclusion drawn from the test that is incorrect.

(a) In a multiple regression of Memory on quantitative variables Age and Health, the independent variable Age was not significant (t=1.42, p=0.166). Hence, Age has no significant relationship with Memory.

(b) In a multiple regression of Memory and quantitative variables Age and Health, the F-test from the ANOVA was significant (F=4.68, p=0.005). Hence, both Age and Health have a significant relationship with memory.