Problem

The high temperature (in degrees Fahrenheit), $x$, and the ice cream sales for a local store, $y$, are related by the regression line equation $\mathrm{y}=8.791 \mathrm{x}-392.966$.

Find the amount of sales predicted by the model if the high temperature is $\mathrm{x}=94^{\circ} \mathrm{F}$. Give your answer as a monetary amount rounded to the nearest cent.
$\$ 238.39$
$\$ 832.39$
$\$ 233.39$
$\$ 433.39$

Answer

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Answer

Final Answer: The predicted sales when the temperature is 94 degrees Fahrenheit is approximately \(\boxed{433.39}\) dollars.

Steps

Step 1 :Given the regression line equation \(y = 8.791x - 392.966\), where \(x\) is the high temperature in degrees Fahrenheit and \(y\) is the ice cream sales for a local store.

Step 2 :We are asked to find the predicted sales when the high temperature is 94 degrees Fahrenheit. This can be found by substituting \(x = 94\) into the regression line equation.

Step 3 :Substituting \(x = 94\) into the equation gives \(y = 8.791(94) - 392.966\).

Step 4 :Solving the equation gives \(y = 433.38800000000003\).

Step 5 :Rounding to the nearest cent gives \(y = 433.39\).

Step 6 :Final Answer: The predicted sales when the temperature is 94 degrees Fahrenheit is approximately \(\boxed{433.39}\) dollars.

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