Solved on Mar 03, 2024

Determine the number of situps a person who watches $11.5$ hours of TV can do, given the linear regression $y =$ - $0.848x + 31.273$ with $r^2 = 0.614656$ and $r = -0.784$ .

STEP 1

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

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 $x$ .
$y = ax + b$

STEP 3

Substitute the given values of $a$ , $b$ , and $x$ into the regression equation.
$y = (-0.848)(11.5) + 31.273$

STEP 4

Multiply the slope $a$ by the value of $x$ .
$y = -0.848 \times 11.5 + 31.273$

STEP 5

Calculate the product of $-0.848$ and $11.5$ .
$y = -9.752 + 31.273$

STEP 6

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

STEP 7

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

STEP 8

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

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Determine the number of situps a person who watches $11.5$ hours of TV can do, given the linear regression $y =$ - $0.848x + 31.273$ with $r^2 = 0.614656$ and $r = -0.784$ .

STEP 1

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 $x$ .
$y = ax + b$

STEP 3

Substitute the given values of $a$ , $b$ , and $x$ into the regression equation.
$y = (-0.848)(11.5) + 31.273$

STEP 4

Multiply the slope $a$ by the value of $x$ .
$y = -0.848 \times 11.5 + 31.273$

STEP 5

Calculate the product of $-0.848$ and $11.5$ .
$y = -9.752 + 31.273$

STEP 6

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

STEP 7

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

STEP 8

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

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Determine the number of situps a person who watches 11.511.511.5 hours of TV can do, given the linear regression y=y = y=-0.848x+31.2730.848x + 31.2730.848x+31.273 with r2=0.614656r^2 = 0.614656r2=0.614656 and r=−0.784r = -0.784r=−0.784.

STEP 1

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 xxx.y=ax+by = ax + by=ax+b

STEP 3

Substitute the given values of aaa, bbb, and xxx into the regression equation.y=(−0.848)(11.5)+31.273y = (-0.848)(11.5) + 31.273y=(−0.848)(11.5)+31.273

STEP 4

Multiply the slope aaa by the value of xxx.y=−0.848×11.5+31.273y = -0.848 \times 11.5 + 31.273y=−0.848×11.5+31.273

STEP 5

Calculate the product of −0.848-0.848−0.848 and 11.511.511.5.y=−9.752+31.273y = -9.752 + 31.273y=−9.752+31.273

STEP 6

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

STEP 7

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

STEP 8

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

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine the number of situps a person who watches $11.5$ hours of TV can do, given the linear regression $y =$ - $0.848x + 31.273$ with $r^2 = 0.614656$ and $r = -0.784$ .

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

Substitute the given values of $a$ , $b$ , and $x$ into the regression equation.
$y = (-0.848)(11.5) + 31.273$

Multiply the slope $a$ by the value of $x$ .
$y = -0.848 \times 11.5 + 31.273$

Calculate the product of $-0.848$ and $11.5$ .
$y = -9.752 + 31.273$

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

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

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