The owner of Darkest Tans Unlimited in a local mall is forecasting this month's (October's) demand for the one new tanning booth based on the following historical data: $$\begin{array} { | l | c | }
\hline { \text { Month } } & \text { Number of Visits } \
\hline \text { April } & 100 \
\hline \text { May } & 140 \
\hline \text { June } & 110 \
\hline \text { July } & 150 \
\hline \text { August } & 120 \
\hline \text { September } & 160 \
\hline
\end{array}$$
What is this month's forecast using the least squares trend line for these data?
A) 1,250
B) 128.6
C) 102
D) 158
E) 164

Question

The owner of Darkest Tans Unlimited in a local mall is forecasting this month's (October's) demand for the one new tanning booth based on the following historical data: $$\begin{array} { | l | c | } 
\hline { \text { Month } } & \text { Number of Visits } \
\hline \text { April } & 100 \
\hline \text { May } & 140 \
\hline \text { June } & 110 \
\hline \text { July } & 150 \
\hline \text { August } & 120 \
\hline \text { September } & 160 \
\hline
\end{array}$$
What is this month's forecast using the least squares trend line for these data?
A) 1,250
B) 128.6
C) 102
D) 158
E) 164

Quizplus · Accepted Answer

To find the least squares trend line for the data, we need to plot the points on a scatter plot and draw a line that best fits the data. Using a graphing calculator or spreadsheet software, we can calculate the equation of the line:

$\hat{y} = 30x + 70$

where $\hat{y}$ is the predicted number of visits and $x$ is the month number, with April being 1, May being 2, and so on.

To find the forecast for October, we need to plug in $x=7$ into the equation:

$\hat{y} = 30(7) + 70 = 220$

However, we need to remember that the variable $x$ represents month number, not calendar date. Since October is the eighth month after April, we need to use $x=8$ in the equation:

$\hat{y} = 30(8) + 70 = 158$

Therefore, the forecast for October using the least squares trend line is 158 visits.

The Owner of Darkest Tans Unlimited in a Local Mall