Solved on Mar 03, 2024

Determine the number of situps a person who watches 11.511.5 hours of TV can do, given the linear regression y=y = -0.848x+31.2730.848x + 31.273 with r2=0.614656r^2 = 0.614656 and r=0.784r = -0.784.

STEP 1

Assumptions
1. The regression equation is given by y=ax+by = ax + b.
2. The slope of the regression line is a=0.848a = -0.848.
3. The y-intercept of the regression line is b=31.273b = 31.273.
4. The coefficient of determination is r2=0.614656r^2 = 0.614656.
5. The correlation coefficient is r=0.784r = -0.784.
6. We are given the value of xx (hours of TV watched per day) as 11.5 hours.
7. We want to predict the value of yy (number of situps) for x=11.5x = 11.5.

STEP 2

To predict the number of situps a person can do, we will use the regression equation and plug in the given value of xx.
y=ax+by = ax + b

STEP 3

Substitute the given values of aa, bb, and xx into the regression equation.
y=(0.848)(11.5)+31.273y = (-0.848)(11.5) + 31.273

STEP 4

Multiply the slope aa by the value of xx.
y=0.848×11.5+31.273y = -0.848 \times 11.5 + 31.273

STEP 5

Calculate the product of 0.848-0.848 and 11.511.5.
y=9.752+31.273y = -9.752 + 31.273

STEP 6

Add the y-intercept bb to the product calculated in the previous step.
y=9.752+31.273y = -9.752 + 31.273

STEP 7

Calculate the predicted value of yy.
y=21.521y = 21.521

STEP 8

Round the predicted value of yy to one decimal place.
y21.5y \approx 21.5
The predicted number of situps a person who watches 11.5 hours of TV can do is approximately 21.5.

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