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?

Explanation:

Step1: Substitute \(x = 80\) into the regression equation

Given the regression equation \(y=-0.96x + 103\), when \(x = 80\), we have \(y=-0.96\times80+103\).
First, calculate \(-0.96\times80=-76.8\). Then, \(y=-76.8 + 103\).

Step2: Calculate the value of \(y\)

\(y=-76.8+103 = 26.2\approx26\) (since we are talking about the number of coats, we round to the nearest whole number).

Step3: Substitute \(y = 125\) into the regression equation and solve for \(x\)

Set \(125=-0.96x + 103\).
First, subtract 103 from both sides: \(125 - 103=-0.96x\). So, \(22=-0.96x\).
Then, solve for \(x\): \(x=\frac{22}{- 0.96}\approx - 22.9\)

Answer:

When the average temperature is \(80^{\circ}F\), the number of coats sold is \(26\). When \(125\) coats are sold, the predicted temperature is \(-22.9^{\circ}F\)