The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the standard error of estimate, $\mathrm { Se }$ given that ? = 0.449x - 30.27. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A)0.935
B)1.162
C)1.007
D)0.815

Question

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the standard error of estimate, $\mathrm { Se }$ given that ? = 0.449x - 30.27. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$
A)0.935
B)1.162
C)1.007
D)0.815

Quizplus · Accepted Answer

The standard error of estimate is the standard deviation of the residuals. The residuals are the differences between the observed values of y and the predicted values of y. The predicted values of y are calculated using the regression equation. The standard deviation of the residuals is calculated using the following formula:$$ \mathrm { Se } = \sqrt { \frac { \sum ( y _ { i } - \hat { y } _ { i } ) ^ { 2 } } { n - 2 } } $$where:* $ y _ { i } $ is the observed value of y* $ \hat { y } _ { i } $ is the predicted value of y* n is the number of observationsIn this case, the regression equation is:$$ \hat { y } = 0.449x - 30.27 $$The residuals are:$$ \begin{array} { l | c | c | c | c | c | c | c | c | c | } \text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \\hline \text { Number of absences, y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5 \\hline \text { Predicted number of absences, } \hat { y } & 2.62 & 6.93 & 9.26 & 8.99 & 8.47 & 12.34 & 3.76 & 13.49 & 6.44 \\hline \text { Residual, } y _ { i } - \hat { y } _ { i } & 0.38 & 0.07 & 0.74 & 1.01 & -0.47 & 2.66 & 0.24 & 1.51 & -1.44\end{array} $$The sum of the squared residuals is:$$ \sum ( y _ { i } - \hat { y } _ { i } ) ^ { 2 } = 10.44 $$The number of observations is:$$ n = 9 $$Therefore, the standard error of estimate is:$$ \mathrm { Se } = \sqrt { \frac { 10.44 } { 9 - 2 } } = 0.935 $$Therefore, the correct answer is A.

The Data Below Are the Temperatures on Randomly Chosen Days Se\mathrm { Se }Se

The Data Below Are the Temperatures on Randomly Chosen Days $\mathrm { Se }$