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.

Question

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