Solved on Dec 05, 2023

Find the best predicted value of the response variable for $x=3.5$ given $r=0.742$ and the regression equation $\hat{y}=55.8+2.79x$ . Round to two decimal places. Use a significance level of 0.05.

STEP 1

Assumptions
1. The given regression equation is $\hat{y}=55.8+2.79x$ .
2. The correlation coefficient is $r=0.742$ .
3. The mean of the response variable $y$ is $\bar{y}=71.125$ .
4. We are asked to predict the value of $y$ for $x=3.5$ .
5. The significance level is $0.05$ .
6. The critical values of the Pearson correlation coefficient $r$ are available if needed for determining the significance of the regression.

STEP 2

To find the best predicted value of the response variable $y$ for a given value of $x$ , we use the regression equation.
$\hat{y} = a + bx$
where $a$ is the y-intercept and $b$ is the slope of the regression line.

STEP 3

Plug in the given value of $x=3.5$ into the regression equation to calculate the predicted value of $y$ .
$\hat{y} = 55.8 + 2.79(3.5)$

STEP 4

Calculate the value inside the parentheses first.
$2.79 \times 3.5 = 9.765$

STEP 5

Now add this value to the y-intercept to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765$

STEP 6

Calculate the sum to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765 = 65.565$

STEP 7

Round the predicted value of $y$ to two decimal places.
$\hat{y} \approx 65.57$
The best predicted value of $y$ for $x=3.5$ is approximately $65.57$ .

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Find the best predicted value of the response variable for $x=3.5$ given $r=0.742$ and the regression equation $\hat{y}=55.8+2.79x$ . Round to two decimal places. Use a significance level of 0.05.

STEP 1

STEP 2

To find the best predicted value of the response variable $y$ for a given value of $x$ , we use the regression equation.
$\hat{y} = a + bx$
where $a$ is the y-intercept and $b$ is the slope of the regression line.

STEP 3

Plug in the given value of $x=3.5$ into the regression equation to calculate the predicted value of $y$ .
$\hat{y} = 55.8 + 2.79(3.5)$

STEP 4

Calculate the value inside the parentheses first.
$2.79 \times 3.5 = 9.765$

STEP 5

Now add this value to the y-intercept to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765$

STEP 6

Calculate the sum to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765 = 65.565$

STEP 7

Round the predicted value of $y$ to two decimal places.
$\hat{y} \approx 65.57$
The best predicted value of $y$ for $x=3.5$ is approximately $65.57$ .

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Find the best predicted value of the response variable for x=3.5x=3.5x=3.5 given r=0.742r=0.742r=0.742 and the regression equation y^=55.8+2.79x\hat{y}=55.8+2.79xy^​=55.8+2.79x. Round to two decimal places. Use a significance level of 0.05.

STEP 1

STEP 2

To find the best predicted value of the response variable yyy for a given value of xxx, we use the regression equation.y^=a+bx\hat{y} = a + bxy^​=a+bxwhere aaa is the y-intercept and bbb is the slope of the regression line.

STEP 3

Plug in the given value of x=3.5x=3.5x=3.5 into the regression equation to calculate the predicted value of yyy.y^=55.8+2.79(3.5)\hat{y} = 55.8 + 2.79(3.5)y^​=55.8+2.79(3.5)

STEP 4

Calculate the value inside the parentheses first.2.79×3.5=9.7652.79 \times 3.5 = 9.7652.79×3.5=9.765

STEP 5

Now add this value to the y-intercept to find the predicted value of yyy.y^=55.8+9.765\hat{y} = 55.8 + 9.765y^​=55.8+9.765

STEP 6

Calculate the sum to find the predicted value of yyy.y^=55.8+9.765=65.565\hat{y} = 55.8 + 9.765 = 65.565y^​=55.8+9.765=65.565

STEP 7

Round the predicted value of yyy to two decimal places.y^≈65.57\hat{y} \approx 65.57y^​≈65.57The best predicted value of yyy for x=3.5x=3.5x=3.5 is approximately 65.5765.5765.57.

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

Find the best predicted value of the response variable for $x=3.5$ given $r=0.742$ and the regression equation $\hat{y}=55.8+2.79x$ . Round to two decimal places. Use a significance level of 0.05.

To find the best predicted value of the response variable $y$ for a given value of $x$ , we use the regression equation.
$\hat{y} = a + bx$
where $a$ is the y-intercept and $b$ is the slope of the regression line.

Plug in the given value of $x=3.5$ into the regression equation to calculate the predicted value of $y$ .
$\hat{y} = 55.8 + 2.79(3.5)$

Calculate the value inside the parentheses first.
$2.79 \times 3.5 = 9.765$

Now add this value to the y-intercept to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765$

Calculate the sum to find the predicted value of $y$ .
$\hat{y} = 55.8 + 9.765 = 65.565$

Round the predicted value of $y$ to two decimal places.
$\hat{y} \approx 65.57$
The best predicted value of $y$ for $x=3.5$ is approximately $65.57$ .