Compute the Sum of Squared Residuals
-The regression line for the given data is $\hat { y } = 6.91 x + 46.26$. Determine the residual of a data point for which $x = 3$ and $\mathrm { y } = 61$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$

A) $- 5.99$
B) $127.99$
C) $66.99$
D) $- 464.77$

Question

Compute the Sum of Squared Residuals
-The regression line for the given data is $\hat { y } = 6.91 x + 46.26$. Determine the residual of a data point for which $x = 3$ and $\mathrm { y } = 61$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}
\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$

A) $- 5.99$
B) $127.99$
C) $66.99$
D) $- 464.77$

Quizplus · Accepted Answer

To find the residual for the data point where $x = 3$ and $y = 61$, we first calculate the predicted value $\hat{y}$ using the regression equation $\hat{y} = 6.91x + 46.26$. For $x = 3$, $\hat{y} = 6.91(3) + 46.26 = 20.73 + 46.26 = 66.99$. The residual is the difference between the actual value $y$ and the predicted value $\hat{y}$, so it is $61 - 66.99 = -5.99$.

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

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