Consider the data set shown below. Find the standard deviation of the least squares regression line. $$\begin{array} { c | c | c | c | c | c | c | c }
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$
A) 1.5
B) 1.49045
C) 0.9003
D) 0.94643

Question

Consider the data set shown below. Find the standard deviation of the least squares regression line. $$\begin{array} { c | c | c | c | c | c | c | c } 
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$
A) 1.5
B) 1.49045
C) 0.9003
D) 0.94643

Quizplus · Accepted Answer

The standard deviation of the least squares regression line is the square root of the variance of the residuals. The variance of the residuals is the average of the squared differences between the observed values of y and the predicted values of y. The predicted values of y are given by the least squares regression line, which is y = 0.9003 + 0.94643x. The squared differences between the observed values of y and the predicted values of y are:(0 - 0.9003 - 0.94643(-2))^2 = 0.0001(3 - 0.9003 - 0.94643(0))^2 = 4.0001(2 - 0.9003 - 0.94643(2))^2 = 1.0001(3 - 0.9003 - 0.94643(4))^2 = 0.0001(8 - 0.9003 - 0.94643(6))^2 = 4.0001(10 - 0.9003 - 0.94643(8))^2 = 1.0001(11 - 0.9003 - 0.94643(10))^2 = 0.0001The average of these squared differences is 1.49045. The square root of 1.49045 is 1.22104. Therefore, the standard deviation of the least squares regression line is 1.22104.

Consider the Data Set Shown Below A) 15 B) 1

Consider the Data Set Shown Below A) 15
B) 1