Scenario 7.3
The Entrepreneurship professor had a habit of oversupplying extra credit opportunities for his class each semester and his colleagues delighted in trying to forecast his class enrollment from one semester to the next.The forecasts for one colleague,along with the actual class enrollment,appear in the table.
$$\begin{array} { | c | c | c | }
\hline \text { Period } & \text { Actual } & \text { Forecast } \
\hline 1 & 173 & 166.7 \
\hline 2 & 177 & 183 \
\hline 3 & 180 & 174.7 \
\hline 4 & 151 & 163.2 \
\hline 5 & 168 & 155.6 \
\hline 6 & 184 & 187.6 \
\hline 7 & 198 & 192.9 \
\hline 8 & 191 & 194.6 \
\hline 9 & 167 & 149.8 \
\hline 10 & 177 & 195.2 \
\hline
\end{array}$$
-Calculate the MSE for this scenario.
A)106.60
B)119.80
C)108.54
D)112.20

Question

Scenario 7.3
The Entrepreneurship professor had a habit of oversupplying extra credit opportunities for his class each semester and his colleagues delighted in trying to forecast his class enrollment from one semester to the next.The forecasts for one colleague,along with the actual class enrollment,appear in the table.
 $$\begin{array} { | c | c | c | } 
\hline \text { Period } & \text { Actual } & \text { Forecast } \
\hline 1 & 173 & 166.7 \
\hline 2 & 177 & 183 \
\hline 3 & 180 & 174.7 \
\hline 4 & 151 & 163.2 \
\hline 5 & 168 & 155.6 \
\hline 6 & 184 & 187.6 \
\hline 7 & 198 & 192.9 \
\hline 8 & 191 & 194.6 \
\hline 9 & 167 & 149.8 \
\hline 10 & 177 & 195.2 \
\hline
\end{array}$$
-Calculate the MSE for this scenario.
A)106.60
B)119.80
C)108.54
D)112.20

Quizplus · Accepted Answer

We can use the formula for calculating Mean Squared Error (MSE):
$$MSE = \frac{\sum\limits_{i=1}^n (Y_i-\hat{Y_i})^2}{n}$$
where $n$ is the number of observations, $Y_i$ is the actual value, $\hat{Y_i}$ is the forecasted value, and $i$ ranges from 1 to $n$.

Using the given data, we can calculate the MSE as follows:
$$MSE = \frac{(173-166.7)^2 + (177-183)^2 + (180-174.7)^2 + (151-163.2)^2 + (168-155.6)^2 + (184-187.6)^2 + (198-192.9)^2 + (191-194.6)^2 + (167-149.8)^2 + (177-195.2)^2}{10}$$
$$MSE \approx 108.54$$
Therefore, the best choice is C.

Scenario 7 -Calculate the MSE for This Scenario