Find the Least-Squares Regression Line and Use the Line to Make Predictions
-The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Find the equation of the regression line for the given data. What would be the predicted pressure if the age was 60 ? Round the predicted pressure to the nearest whole number.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\text { Age, } \mathrm{x} & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm{y} & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$

A) $\hat { y } = 1.488 x + 60.46 ; 150 \mathrm {~mm}$
B) $\hat {y} = 60.46 x - 1.488 ; 3626 \mathrm {~mm}$
C) $\hat {y} = 1.448 \mathrm { x } - 60.46 ; 29 \mathrm {~mm}$
D) $\hat {y} = 60.46 x + 1.488 ; 3629 \mathrm {~mm}$

Question

Find the Least-Squares Regression Line and Use the Line to Make Predictions
-The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Find the equation of the regression line for the given data. What would be the predicted pressure if the age was 60 ? Round the predicted pressure to the nearest whole number.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\text { Age, } \mathrm{x} & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm{y} & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$

A) $\hat { y } = 1.488 x + 60.46 ; 150 \mathrm {~mm}$
B) $\hat {y} = 60.46 x - 1.488 ; 3626 \mathrm {~mm}$
C) $\hat {y} = 1.448 \mathrm { x } - 60.46 ; 29 \mathrm {~mm}$
D) $\hat {y} = 60.46 x + 1.488 ; 3629 \mathrm {~mm}$

Quizplus · Accepted Answer

The least-squares regression line is calculated using the formula $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The correct equation, based on the given data, is $\hat{y} = 1.488x + 60.46$. Using this equation to predict the pressure at age 60 gives a value of approximately 150 mmHg, after rounding to the nearest whole number.