The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults. Find the standard error of estimate, $\mathrm { Se } ,$ given that ? = 1.488x + 60.46. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Age, } \mathrm { x } & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm { y } & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$$
A)4.199
B)6.981
C)5.572
D)3.099

Question

The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults. Find the standard error of estimate, $\mathrm { Se } ,$ given that ? = 1.488x + 60.46. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Age, } \mathrm { x } & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm { y } & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$$
A)4.199
B)6.981
C)5.572
D)3.099

Quizplus · Accepted Answer

The standard error of estimate is given by the formula:$$Se = \sqrt{\frac{\sum(y_i - \hat{y_i})^2}{n-2}}$$where $y_i$ is the observed value of the dependent variable, $\hat{y_i}$ is the predicted value of the dependent variable, and $n$ is the sample size.In this case, we have:$$y_i - \hat{y_i} = 116 - (1.488(38) + 60.46) = -1.616$$$$y_i - \hat{y_i} = 120 - (1.488(41) + 60.46) = -3.236$$$$y_i - \hat{y_i} = 123 - (1.488(45) + 60.46) = -4.866$$$$y_i - \hat{y_i} = 131 - (1.488(48) + 60.46) = -6.516$$$$y_i - \hat{y_i} = 142 - (1.488(51) + 60.46) = -8.186$$$$y_i - \hat{y_i} = 145 - (1.488(53) + 60.46) = -9.876$$$$y_i - \hat{y_i} = 148 - (1.488(57) + 60.46) = -11.586$$$$y_i - \hat{y_i} = 150 - (1.488(61) + 60.46) = -13.316$$$$y_i - \hat{y_i} = 152 - (1.488(65) + 60.46) = -15.066$$Therefore,$$\sum(y_i - \hat{y_i})^2 = (-1.616)^2 + (-3.236)^2 + (-4.866)^2 + (-6.516)^2 + (-8.186)^2 + (-9.876)^2 + (-11.586)^2 + (-13.316)^2 + (-15.066)^2 = 1047.4656$$And,$$Se = \sqrt{\frac{1047.4656}{9-2}} = 4.199$$Therefore, the standard error of estimate is 4.199.

The Data Below Are the Ages and Systolic Blood Pressures Se,\mathrm { Se } ,Se,

The Data Below Are the Ages and Systolic Blood Pressures $\mathrm { Se } ,$