Which of the followings is correct in a simple linear regression? Choose all cor

Question

Which of the followings is correct in a simple linear regression? Choose all correct answers. a. MSE always provides an unbiased estimate of sigma^2, the error variance in a simple linear regression. b. MSR also provides an unbiased estimate of sigma^2 if there is no true linear regression line of Y on X, i.e. beta_1 = 0. c. MSR in a simple linear regression is equal to SSR, an amount of total variation in Y explained by the regression on X. d. If there exists a true linear regression of Y on X, i.e. beta_1 not equal to 0, MSR will tend to be larger than MSE, providing an overestimation of sigma^2. e. The ratio SSR/SST the same whether Y is regressed on X, or X is regressed on Y. Which of the followings is correct? Choose all correct answers. a. The least squares method determines the best fitting straight line as the line that minimizes the sum of squares of the lengths of the shortest line segments drawn from the observed data points on the scatter diagram to the fitted line. b. The least squares line may be used to determine predicted Y values that correspond to actually observed X values only. c. As the fit gets worse, the sum of squared errors gets large. d. Under the 5 assumptions for a simple linear regression, the estimators of intercept and slope are t distributed. e. For any fixed value of X, Y has a normal distribution. Which of the followings is correct? Choose all correct answers. a. Whether or not the hypothesis H_0: beta_1 = 0 is rejected, a simple linear regression model may not be appropriate. b. If H_0: beta_0 = 0 is rejected, we conclude that the predicted value of Y at X = 0 is equal to 0. c. The prediction interval of a new value of Y is not always larger than the confidence interval of mean of Y. d. If H_0: beta_1 = 0 is rejected, it is possible that we committed a Type II error. e. If H_0: beta_0 = 0 is not rejected, it is possible that we committed a Type I error. Which of the followings is correct about the sample linear correlation coefficient r and the population in car correlation coefficient rho, between X and Y? Choose all correct answers. a. A test of H_0: rho = 0 Ls mathematically equivalent to the test of H_0: beta_1. b. If r is positive, beta_1 must also be positive. c. If r is close to 0, there is little association between two variables. d. If r^2 is 0. it means that using X offers no improvement in predicting Y. e. r^2 is a measure of non-linear association between two variables.

Explanation / Answer

1) in this there are only two correct statements because and those are statement A AND C

as the statement b,d and e are error statements and not correctly given while the statement A AND C ARE THE FACTUAL DATA WHICH ARE ALWAYS CORRECT IN RESPECT TO THE REGRESSION

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