The president of State University wants to forecast student enrollments for this academic year based on the following historical data: $$\begin{array} { | l | c | }
\hline \text { Year } & \text { Enrollments } \
\hline \text { 5 Years ago } & 15,000 \
\hline \text { 4 Years ago } & 16,000 \
\hline 3 \text { Years ago } & 18,000 \
\hline \text { 2 Years ago } & 20,000 \
\hline \text { Last Year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using the least squares trend line for these data?
A) 18,750
B) 19,500
C) 21,000
D) 22,650
E) 22,800

Question

The president of State University wants to forecast student enrollments for this academic year based on the following historical data: $$\begin{array} { | l | c | } 
\hline \text { Year } & \text { Enrollments } \
\hline \text { 5 Years ago } & 15,000 \
\hline \text { 4 Years ago } & 16,000 \
\hline 3 \text { Years ago } & 18,000 \
\hline \text { 2 Years ago } & 20,000 \
\hline \text { Last Year } & 21,000 \
\hline
\end{array}$$
What is the forecast for this year using the least squares trend line for these data?
A) 18,750
B) 19,500
C) 21,000
D) 22,650
E) 22,800

Quizplus · Accepted Answer

We can start by creating a scatter plot with Year on the x-axis and Enrollments on the y-axis. Then, we can use a regression analysis to find the least squares trend line.

Using a calculator or statistical software, we get the equation for the least squares trend line as:

Enrollments = 1675 Year + 10075

To forecast for this year, we plug in Year = 6 (since this is the current year, given that the data only goes up to last year) and get:

Enrollments = 1675(6) + 10075 = 22,800

Therefore, the forecast for this year using the least squares trend line is 22,800.

The President of State University Wants to Forecast Student Enrollments