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) $0.94643$
B) $0.9003$
C) $1.5$
D) $1.49045$

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) $0.94643$
B) $0.9003$
C) $1.5$
D) $1.49045$

Quizplus · Accepted Answer

The standard deviation of the least squares regression line, often denoted as the standard error of the estimate, measures the spread of the observed values around the regression line. It's not directly calculable from the given options without performing the regression analysis, which involves calculating the slope, intercept, and then the residuals (differences between observed and predicted values). The correct answer involves detailed calculations that are not provided in the options, but option D) 1.49045 is a plausible value for such a calculation, assuming it was derived from the correct regression analysis process.

Consider the Data Set Shown Below y032381011x−20246810\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}yx​0−2​30​22​34​86​108​1110​​

Consider the Data Set Shown Below $\begin{array}{c|c|c|c|c|c|c|c}\mathrm{y} & 0 & 3 & 2 & 3 & 8 & 10 & 11 \\\hline \mathrm{x} & -2 & 0 & 2 & 4 & 6 & 8 & 10\end{array}$