Provide answers and explanations;

1. Suppose we regress SAT score on parent's education and parent's income. If we run the regression again but also include the student's GPA as an additional regressor: (a) The R' for the regression will either stay the same or increase. (b) The adjusted R' for the regression will either stay the same or increase. (c) Both (a) and (b) are true. (d) Neither (a) nor (b) is true.2. Suppose we have a sample of the heights of Davis students and want to use the sample mean to get a confidence interval for the mean height in the population. Which of the following would increase the width of this confidence interval? (a) Switching from a 95% confidence interval to a 90% confidence interval. (b) Increasing the sample size used to calculate the sample mean. (c) Switching from a 95% confidence interval to a 99% confidence interval. (d) All of the above.3. Suppose we can reject the null hypothesis that 82 2 0 at a 5% significance level where 82 is the slope coefficient from a bivariate regression. Which of the following is definitely true? (a) Our test statistic was negative. (b) We can reject the null hypothesis that 82 = 0 at a 5% significance level. (c) We can reject the null hypothesis that 82 2 0 at a 2.5% significance level. (d) We can reject the null hypothesis that 82 -10. (d) E(b2)