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(6) The OLS estimator is derived by A) drawing the estimated regression line connecting the $Y_i$ corresponding to the lowest $X_i$ observation with the $Y_i$ corresponding to the highest $X_i$ observation. B) minimizing the sum of absolute residuals. C) minimizing the sum of squared residuals. D) minimizing the standard error of the estimator. (7) The OLS residuals, $U_i$ are defined as A) $Y_i - eta_0 - eta_1X_i$. B) $Y_i - hat{Y}_i$. C) $hat{Y}_i - eta_0 - eta_1X_i$. D) $hat{Y}_i - Y_i$. (8) The regression $R^2$ is a measure of A) whether or not X causes Y. B) whether or not X and Y are correlated. C) the goodness-of-fit of your regression line. D) whether or not ESS > TSS. (9) When the estimated coefficient $eta_1$ is zero in a simple regression model, then A) $R^2 = Y$. B) $R^2 = 0$. C) $R^2 = 1$. D) $0 < R^2 < 1$. (10) Which of the following statements is correct? A) ESS > TSS. B) ESS = SSR + TSS. C) TSS = ESS + SSR. D) $R^2 = 1 - (ESS/TSS)$.

          (6) The OLS estimator is derived by
A) drawing the estimated regression line connecting the $Y_i$ corresponding to the lowest $X_i$ observation
with the $Y_i$ corresponding to the highest $X_i$ observation.
B) minimizing the sum of absolute residuals.
C) minimizing the sum of squared residuals.
D) minimizing the standard error of the estimator.
(7) The OLS residuals, $U_i$ are defined as
A) $Y_i - eta_0 - eta_1X_i$.
B) $Y_i - hat{Y}_i$.
C) $hat{Y}_i - eta_0 - eta_1X_i$.
D) $hat{Y}_i - Y_i$.
(8) The regression $R^2$ is a measure of
A) whether or not X causes Y.
B) whether or not X and Y are correlated.
C) the goodness-of-fit of your regression line.
D) whether or not ESS > TSS.
(9) When the estimated coefficient $eta_1$ is zero in a simple regression model, then
A) $R^2 = Y$.
B) $R^2 = 0$.
C) $R^2 = 1$.
D) $0 < R^2 < 1$.
(10) Which of the following statements is correct?
A) ESS > TSS.
B) ESS = SSR + TSS.
C) TSS = ESS + SSR.
D) $R^2 = 1 - (ESS/TSS)$.

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(6) The OLS estimator is derived by
A) drawing the estimated regression line connecting the Yi corresponding to the lowest Xi observation
with the Yi corresponding to the highest Xi observation.
B) minimizing the sum of absolute residuals.
C) minimizing the sum of squared residuals.
D) minimizing the standard error of the estimator.
(7) The OLS residuals, Ui are defined as
A) Yi - eta0 - eta1Xi.
B) Yi - hatYi.
C) hatYi - eta0 - eta1Xi.
D) hatYi - Yi.
(8) The regression R^2 is a measure of
A) whether or not X causes Y.
B) whether or not X and Y are correlated.
C) the goodness-of-fit of your regression line.
D) whether or not ESS > TSS.
(9) When the estimated coefficient eta1 is zero in a simple regression model, then
A) R^2 = Y.
B) R^2 = 0.
C) R^2 = 1.
D) 0 < R^2 < 1.
(10) Which of the following statements is correct?
A) ESS > TSS.
B) ESS = SSR + TSS.
C) TSS = ESS + SSR.
D) R^2 = 1 - (ESS/TSS).

Added by Brandy S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Benjamin Densmore

Step 1

So, the correct option is C. (7) The OLS residuals, $u_i$, are defined as the difference between the actual value of the dependent variable, $Y_i$, and the predicted value, $\hat{Y}_i$. So, the correct option is B. (8) The regression R-squared is a measure of Show more…

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