Question

A graph has average temperature (degrees Fahrenheit) on the x-axis, from 0 to 60, and total coat sales on the y-axis, from 0 to 100. A trend line goes through points (55, 50) and (65, 40). The regression equation is y = negative 0.96 x + 103.
Use the regression for Clothes-4-You coat sales to make predictions.

How many coats should Clothes-4-You expect to sell when the average temperature is 80°F?

What is the predicted temperature when 125 coats are sold?

Answer 1

To predict coat sales or temperatures using the regression equation \( y = -0.96x + 103 \), we can substitute the values accordingly.

1. **Predicted coat sales when the average temperature is 80°F:**

Plug \( x = 80 \) into the regression equation:

\[
y = -0.96(80) + 103
\]

Now, calculate:

\[
y = -76.8 + 103 = 26.2
\]

Therefore, Clothes-4-You should expect to sell approximately **26 coats** when the average temperature is 80°F.

2. **Predicted temperature when 125 coats are sold:**

To find the temperature when \( y = 125 \), set up the equation:

\[
125 = -0.96x + 103
\]

Now, solve for \( x \):

\[
-0.96x = 125 - 103
\]
\[
-0.96x = 22
\]
\[
x = -\frac{22}{0.96} \approx -22.92
\]

Therefore, the predicted temperature when 125 coats are sold is approximately **-22.92°F**.

So the two results are:
- Expected coat sales at 80°F: **26 coats**
- Predicted temperature for 125 coats: **-22.92°F**