Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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 is [tex]$\hat{Y} = 2 + 0.9X$[/tex].

1. For a browsing time of 25 minutes resulting in an amount of [tex]$44.5, what is the predicted amount spent?

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

2. For a browsing time of 30 minutes resulting in an amount spent of $[/tex]27.29, what is the predicted amount spent?

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

3. For a browsing time of 28 minutes resulting in an amount spent of $27.2, what is the predicted amount spent?

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

Sagot :

GinnyAnswer
Sure, let's solve this step-by-step.

1. Predicted Amount for 25 Minutes:
- Given browsing time, [tex]\( X = 25 \)[/tex] minutes.
- Regression equation: [tex]\(\hat{Y} = 2 + 0.9X\)[/tex].

Substitute [tex]\( X = 25 \)[/tex] into the equation:
[tex]\[ \hat{Y} = 2 + 0.9 \times 25 = 2 + 22.5 = 24.5 \text{ dollars} \][/tex]

- Observed amount spent, [tex]\( s = 44.5 \)[/tex] dollars.

Compare the observed amount to the predicted amount:
[tex]\[ 44.5 \text{ (observed)} > 24.5 \text{ (predicted)} \][/tex]
This means the observed value is above the regression line.


2. Predicted Amount for 30 Minutes:
- Given browsing time, [tex]\( X = 30 \)[/tex] minutes.
- Regression equation: [tex]\(\hat{Y} = 2 + 0.9X\)[/tex].

Substitute [tex]\( X = 30 \)[/tex] into the equation:
[tex]\[ \hat{Y} = 2 + 0.9 \times 30 = 2 + 27 = 29 \text{ dollars} \][/tex]

- Observed amount spent, [tex]\( s = 27.29 \)[/tex] dollars.

Compare the observed amount to the predicted amount:
[tex]\[ 27.29 \text{ (observed)} < 29 \text{ (predicted)} \][/tex]
This means the observed value is below the regression line.


3. Predicted Amount for 28 Minutes:
- Given browsing time, [tex]\( X = 28 \)[/tex] minutes.
- Regression equation: [tex]\(\hat{Y} = 2 + 0.9X\)[/tex].

Substitute [tex]\( X = 28 \)[/tex] into the equation:
[tex]\[ \hat{Y} = 2 + 0.9 \times 28 = 2 + 25.2 = 27.2 \text{ dollars} \][/tex]

- Observed amount spent, [tex]\( s = 27.2 \)[/tex] dollars.

Compare the observed amount to the predicted amount:
[tex]\[ 27.2 \text{ (observed)} = 27.2 \text{ (predicted)} \][/tex]
This means the observed value is on the regression line.

### Summary of Results:
1. Browsing time of 25 minutes:
- Predicted amount spent: [tex]\( 24.5 \)[/tex] dollars.
- Observed value in relation to the regression line: Above.

2. Browsing time of 30 minutes:
- Predicted amount spent: [tex]\( 29 \)[/tex] dollars.
- Observed value in relation to the regression line: Below.

3. Browsing time of 28 minutes:
- Predicted amount spent: [tex]\( 27.2 \)[/tex] dollars.
- Observed value in relation to the regression line: On the regression line.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.