The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the standard error of estimate, $\mathrm { Se } $ given that ? = 5.044x + 56.11. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | }
\text { Hours, } \mathrm { x } & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \
\hline \text { Scores, y } & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71
\end{array}$$
A)6.305
B)7.913
C)8.912
D)9.875

Question

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the standard error of estimate, $\mathrm { Se } $ given that ? = 5.044x + 56.11. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | } 
\text { Hours, } \mathrm { x } & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \
\hline \text { Scores, y } & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71
\end{array}$$
A)6.305
B)7.913
C)8.912
D)9.875

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 the dependent variable and the values predicted by the regression line. The standard error of estimate is calculated as the square root of the mean squared error. The mean squared error is the average of the squared residuals.The mean squared error is calculated as:```MSE = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y}_i)^2```where:* n is the number of observations* y_i is the observed value of the dependent variable for observation i* \hat{y}_i is the predicted value of the dependent variable for observation iThe standard error of estimate is calculated as:```Se = \sqrt{MSE}```The standard error of estimate is 6.305.

The Data Below Are the Final Exam Scores of 10 Se\mathrm { Se } Se

The Data Below Are the Final Exam Scores of 10 $\mathrm { Se }$