With reason

5.1. State with reason whether the following statements are true, false, or uncertain. Be precise. a. The t test of significance discussed in this chapter requires that the sampling distributions of estimators B, and , follow the normal distribution. b. Even though the disturbance term in the CLRM is not normally distributed, the OLS estimators are still unbiased. c. If there is no intercept in the regression model, the estimated u:( = ;) will not sum to zero. d. The p value and the size of a test statistic mean the same thing. e. In a regression model that contains the intercept, the sum of the residuals is always zero. f. If a null hypothesis is not rejected, it is true. g. The higher the value of o?, the larger is the variance of 81 given in Eq. (3.3.1). h. The conditional and unconditional means of a random variable are the same things. i. In the two-variable PRF, if the slope coefficient B2 is zero, the intercept B, is estimated by the sample mean 7. j. The conditional variance, var (Y;|X;) = o?, and the unconditional variance of Y, var(Y) = 0;, will be the same if X had no influence on Y. 5.1. State with reason whether the following statements are true, false, or uncertain. Be precise. a. The t test of significance discussed in this chapter requires that the sampling distributions of estimators B, and , follow the normal distribution. b. Even though the disturbance term in the CLRM is not normally distributed, the OLS estimators are still unbiased. c. If there is no intercept in the regression model, the estimated u:( = ;) will not sum to zero. d. The p value and the size of a test statistic mean the same thing. e. In a regression model that contains the intercept, the sum of the residuals is always zero. f. If a null hypothesis is not rejected, it is true. g. The higher the value of o?, the larger is the variance of 81 given in Eq. (3.3.1). h. The conditional and unconditional means of a random variable are the same things. i. In the two-variable PRF, if the slope coefficient B2 is zero, the intercept B, is estimated by the sample mean 7. j. The conditional variance, var (Y;|X;) = o?, and the unconditional variance of Y, var(Y) = 0;, will be the same if X had no influence on Y