Compute the Sum of Squared Residuals
-In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in a 15 minute time period following the addition of food. The data showing the weekly number of grunts and the age of the warthog (in days) are listed below. Compute the sum of the squared residuals of the least squared line for the given data. $\begin{array}{|c|c|c|}
\hline \text { Week } & \begin{array}{c}
\text { Number of } \
\text { Grunts }
\end{array} & \text { Age (days) } \
\hline 1 & 90 & 125 \
\hline 2 & 68 & 141 \
\hline 3 & 39 & 155 \
\hline 4 & 44 & 160 \
\hline 5 & 63 & 167 \
\hline 6 & 40 & 174 \
\hline 7 & 62 & 183 \
\hline 8 & 17 & 189 \
\hline 9 & 20 & 195 \
\hline
\end{array}$

A) $5533.53$
B) $188.84$
C) $74.39$
D) $13.74$

Question

Compute the Sum of Squared Residuals
-In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in a 15 minute time period following the addition of food. The data showing the weekly number of grunts and the age of the warthog (in days) are listed below. Compute the sum of the squared residuals of the least squared line for the given data. $\begin{array}{|c|c|c|}
\hline \text { Week } & \begin{array}{c}
\text { Number of } \
\text { Grunts }
\end{array} & \text { Age (days) } \
\hline 1 & 90 & 125 \
\hline 2 & 68 & 141 \
\hline 3 & 39 & 155 \
\hline 4 & 44 & 160 \
\hline 5 & 63 & 167 \
\hline 6 & 40 & 174 \
\hline 7 & 62 & 183 \
\hline 8 & 17 & 189 \
\hline 9 & 20 & 195 \
\hline
\end{array}$

A) $5533.53$
B) $188.84$
C) $74.39$
D) $13.74$

Quizplus · Accepted Answer

The sum of the squared residuals is the sum of the squared differences between the observed values and the predicted values. The predicted values are obtained by plugging the values of the independent variable into the least squares line. The least squares line for the given data is:$$y = -0.37x + 104.6$$The sum of the squared residuals is:$$SSR = \sum_{i=1}^n (y_i - \hat{y}_i)^2$$$$= (90 - 87.85)^2 + (68 - 81.29)^2 + (39 - 74.73)^2 + (44 - 71.17)^2 + (63 - 67.61)^2 + (40 - 64.05)^2 + (62 - 60.49)^2 + (17 - 56.93)^2 + (20 - 53.37)^2$$$$= 5533.53$$Therefore, the sum of the squared residuals is 5533.53.

Compute the Sum of Squared Residuals -In a Study of Feeding

Compute the Sum of Squared Residuals
-In a Study of Feeding