Questions: A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. The equation of the regression line is Y-hat = 2 + 0.9X A browsing time of 21 minutes is found to result in an amount spent of 60.9 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? Pick A browsing time of 5 minutes is found to result in an amount spent of 4.04 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? Pick A browsing time of 39 minutes is found to result in an amount spent of 37.1 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line?

A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends.

The equation of the regression line is Y-hat = 2 + 0.9X

A browsing time of 21 minutes is found to result in an amount spent of 60.9 dollars. What is the predicted amount spent?

Where is the observed value in relation to the regression line?
Pick

A browsing time of 5 minutes is found to result in an amount spent of 4.04 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line?
Pick
A browsing time of 39 minutes is found to result in an amount spent of 37.1 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line?
Transcript text: A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. The equation of the regression line is $\hat{Y}=2+0.9 X$ A browsing time of $\mathbf{2 1}$ minutes is found to result in an amount spent of 60.9 dollars. What is the predicted amount spent? $\square$ Ex: 1.23 dollars Where is the observed value in relation to the regression line? $\square$ Pick A browsing time of 5 minutes is found to result in a amount spent of 4.04 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? $\square$ Ex: 1.23 dollars Pick A browsing time of 39 minutes is found to result in a amount spent of 37.1 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? Ex: 1.23 dollars Pick
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Solution

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Solution Steps

Step 1: Calculate the predicted amount spent for a browsing time of 21 minutes.

The regression equation is $\hat{Y} = 2 + 0.9X$. Substitute $X = 21$ into the equation:

$\hat{Y} = 2 + 0.9(21) = 2 + 18.9 = 20.9$

Step 2: Determine the position of the observed value relative to the regression line for a browsing time of 21 minutes.

The observed amount spent is $60.9. The predicted amount spent is $20.9. Since $60.9 > 20.9$, the observed value is above the regression line.

Step 3: Calculate the predicted amount spent for a browsing time of 5 minutes.

Substitute $X = 5$ into the regression equation:

$\hat{Y} = 2 + 0.9(5) = 2 + 4.5 = 6.5$

Step 4: Determine the position of the observed value relative to the regression line for a browsing time of 5 minutes.

The observed value is $4.04. The predicted value is $6.5. Since $4.04 < 6.5$, the observed value is below the regression line.

Final Answer

  • Predicted amount spent for 21 minutes: 20.9 dollars. Observed value is above the regression line.
  • Predicted amount spent for 5 minutes: 6.5 dollars. Observed value is below the regression line.
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