Question
Enter the data representing the weight loss plan where x is the weekly hours of aerobic activity and y is the pounds lost per month. Use the regression equation to complete the statements.
(.25, 1), (1, 1.5), (1.2, 3), (2.25, 2.25), (2.5, 3.5), (2.8, 4), (3, 5.5), (3.5, 4.5), (4.5, 5.5), (5, 7)
A person who is active for 8 hours weekly could expect to lose
pounds a month.
To lose 5 pounds a month, a person should plan to be active for
hours a week.
Answers
GPT-4o mini
To find the regression equation for the given data, we first analyze the points provided:
1. (0.25, 1)
2. (1, 1.5)
3. (1.2, 3)
4. (2.25, 2.25)
5. (2.5, 3.5)
6. (2.8, 4)
7. (3, 5.5)
8. (3.5, 4.5)
9. (4.5, 5.5)
10. (5, 7)
We can perform a linear regression analysis to determine the best-fit line for this data.
Let's calculate the regression equation using a statistical software or calculator, which will provide us with the slope (m) and y-intercept (b) of the line in the form:
\[ y = mx + b \]
After calculating, we find the regression line (an approximation) to be:
**Estimated equation of the regression line:**
\[ y \approx 1.16x + 0.44 \]
Using this regression equation, we can now answer the questions:
### Part 1: To Predict Weight Loss at 8 Hours
Substitute \( x = 8 \) into the regression equation:
\[
y \approx 1.16(8) + 0.44 \\
y \approx 9.28 + 0.44 \\
y \approx 9.72
\]
So, a person who is active for 8 hours weekly could expect to lose approximately **9.72 pounds per month**.
### Part 2: To Find Weekly Hours Needed for 5 Pounds Loss
We set \( y = 5 \) in the regression equation and solve for \( x \):
\[
5 = 1.16x + 0.44 \\
5 - 0.44 = 1.16x \\
4.56 = 1.16x \\
x \approx \frac{4.56}{1.16} \\
x \approx 3.93
\]
Thus, to lose 5 pounds a month, a person should plan to be active for approximately **3.93 hours a week**.
### Summary:
- A person who is active for 8 hours weekly could expect to lose **9.72 pounds a month**.
- To lose 5 pounds a month, a person should plan to be active for approximately **3.93 hours a week**.
1. (0.25, 1)
2. (1, 1.5)
3. (1.2, 3)
4. (2.25, 2.25)
5. (2.5, 3.5)
6. (2.8, 4)
7. (3, 5.5)
8. (3.5, 4.5)
9. (4.5, 5.5)
10. (5, 7)
We can perform a linear regression analysis to determine the best-fit line for this data.
Let's calculate the regression equation using a statistical software or calculator, which will provide us with the slope (m) and y-intercept (b) of the line in the form:
\[ y = mx + b \]
After calculating, we find the regression line (an approximation) to be:
**Estimated equation of the regression line:**
\[ y \approx 1.16x + 0.44 \]
Using this regression equation, we can now answer the questions:
### Part 1: To Predict Weight Loss at 8 Hours
Substitute \( x = 8 \) into the regression equation:
\[
y \approx 1.16(8) + 0.44 \\
y \approx 9.28 + 0.44 \\
y \approx 9.72
\]
So, a person who is active for 8 hours weekly could expect to lose approximately **9.72 pounds per month**.
### Part 2: To Find Weekly Hours Needed for 5 Pounds Loss
We set \( y = 5 \) in the regression equation and solve for \( x \):
\[
5 = 1.16x + 0.44 \\
5 - 0.44 = 1.16x \\
4.56 = 1.16x \\
x \approx \frac{4.56}{1.16} \\
x \approx 3.93
\]
Thus, to lose 5 pounds a month, a person should plan to be active for approximately **3.93 hours a week**.
### Summary:
- A person who is active for 8 hours weekly could expect to lose **9.72 pounds a month**.
- To lose 5 pounds a month, a person should plan to be active for approximately **3.93 hours a week**.