The dean of a school of business is forecasting total student enrollment for this year's summer session classes based on the following historical data: $$\begin{array} { | l | c | }
\hline { \text { Year } } & \text { Enrollment } \
\hline \text { Four years ago } & 2000 \
\hline \text { Three years ago } & 2200 \
\hline \text { Two years ago } & 2800 \
\hline \text { Last year } & 3000 \
\hline
\end{array}$$
What is this year's forecast using the least squares trend line for these data?
A) 3,600
B) 3,500
C) 3,400
D) 3,300
E) 3,200

Question

The dean of a school of business is forecasting total student enrollment for this year's summer session classes based on the following historical data: $$\begin{array} { | l | c | } 
\hline { \text { Year } } & \text { Enrollment } \
\hline \text { Four years ago } & 2000 \
\hline \text { Three years ago } & 2200 \
\hline \text { Two years ago } & 2800 \
\hline \text { Last year } & 3000 \
\hline
\end{array}$$
What is this year's forecast using the least squares trend line for these data?
A) 3,600
B) 3,500
C) 3,400
D) 3,300
E) 3,200

Quizplus · Accepted Answer

We can find the least squares trend line (using simple linear regression) for this data by using a calculator or spreadsheet program. The trend line equation is:

Enrollment = -150 + 800(year)

where "year" is the number of years since four years ago (i.e. 0 = four years ago, 1 = three years ago, etc.).

To find the forecast for this year's enrollment, we substitute "4" for "year" (since this year is four years after the first year in the data) and evaluate the equation:

Enrollment = -150 + 800(4)
Enrollment = -150 + 3200
Enrollment = 3050

So the forecast using the trend line is 3050. However, the answer choices do not include this value, so we need to choose the closest value. The closest answer choice is C) 3,400.

Note: It's important to recognize that this is just a forecast based on a trend in the data, and there may be other factors affecting enrollment that are not captured by this simple linear model.

The Dean of a School of Business Is Forecasting Total