Compute the Sum of Squared Residuals
-The regression line for the given data is $\hat { y } = 1.488 x + 60.46$. Determine the residual of a data point for which $x =$ 65 and $y = 152$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\hline \text { Age, } \mathrm{x} & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm{y} & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$

A) $- 5.18$
B) $309.18$
C) $157.18$
D) $- 221.636$

Question

Compute the Sum of Squared Residuals
-The regression line for the given data is $\hat { y } = 1.488 x + 60.46$. Determine the residual of a data point for which $x =$ 65 and $y = 152$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\hline \text { Age, } \mathrm{x} & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm{y} & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$

A) $- 5.18$
B) $309.18$
C) $157.18$
D) $- 221.636$

Quizplus · Accepted Answer

To find the residual for the data point where $x = 65$ and $y = 152$, we first calculate the predicted value $\hat{y}$ using the regression equation $\hat{y} = 1.488x + 60.46$. Substituting $x = 65$, we get $\hat{y} = 1.488(65) + 60.46 = 156.18$. The residual is the difference between the actual value $y$ and the predicted value $\hat{y}$, so it is $152 - 156.18 = -4.18$. However, given the choices, it seems there might be a slight error in the calculation or in the options provided. The closest option to the correct calculation is A) -5.18, assuming a minor discrepancy in calculation or transcription.

Compute the Sum of Squared Residuals -The Regression Line for the Given

Compute the Sum of Squared Residuals
-The Regression Line for the Given