Solved on Dec 12, 2023

Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

STEP 1

Assumptions
1. The linear regression equation is given by $\hat{y}=11+0.5x$ .
2. $\hat{y}$ is the predicted final-exam score.
3. $x$ is the score on the first test.
4. Janelle scored 90 on the first test.
5. The actual final-exam score for Janelle is 60.

STEP 2

To find the predicted value of Janelle's score on the final exam, we need to substitute the score of the first test ( $x$ ) into the linear regression equation.
$\hat{y}=11+0.5x$

STEP 3

Substitute $x = 90$ into the equation to calculate the predicted final-exam score.
$\hat{y}=11+0.5(90)$

STEP 4

Perform the multiplication.
$\hat{y}=11+45$

STEP 5

Add the values to find the predicted final-exam score.
$\hat{y}=11+45=56$
The predicted value of Janelle's score on the final exam is 56.

STEP 6

To find the residual, we need to subtract the predicted final-exam score from the actual final-exam score.
$Residual = Actual\, score - Predicted\, score$

STEP 7

Substitute the actual score (60) and the predicted score (56) into the formula to calculate the residual.
$Residual = 60 - 56$

STEP 8

Calculate the residual.
$Residual = 60 - 56 = 4$
The value of the residual is 4.

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Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

STEP 1

Assumptions
1. The linear regression equation is given by $\hat{y}=11+0.5x$ .
2. $\hat{y}$ is the predicted final-exam score.
3. $x$ is the score on the first test.
4. Janelle scored 90 on the first test.
5. The actual final-exam score for Janelle is 60.

STEP 2

To find the predicted value of Janelle's score on the final exam, we need to substitute the score of the first test ( $x$ ) into the linear regression equation.
$\hat{y}=11+0.5x$

STEP 3

Substitute $x = 90$ into the equation to calculate the predicted final-exam score.
$\hat{y}=11+0.5(90)$

STEP 4

Perform the multiplication.
$\hat{y}=11+45$

STEP 5

Add the values to find the predicted final-exam score.
$\hat{y}=11+45=56$
The predicted value of Janelle's score on the final exam is 56.

STEP 6

To find the residual, we need to subtract the predicted final-exam score from the actual final-exam score.
$Residual = Actual\, score - Predicted\, score$

STEP 7

Substitute the actual score (60) and the predicted score (56) into the formula to calculate the residual.
$Residual = 60 - 56$

STEP 8

Calculate the residual.
$Residual = 60 - 56 = 4$
The value of the residual is 4.

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Predict Janelle's final exam score using the linear regression equation y^=11+0.5x\hat{y}=11+0.5\mathrm{x}y^​=11+0.5x where x=90\mathrm{x}=90x=90. Calculate the residual between the predicted and actual final exam scores.

STEP 1

Assumptions1. The linear regression equation is given by y^=11+0.5x\hat{y}=11+0.5xy^​=11+0.5x.2. y^\hat{y}y^​ is the predicted final-exam score.3. xxx is the score on the first test.4. Janelle scored 90 on the first test.5. The actual final-exam score for Janelle is 60.

STEP 2

To find the predicted value of Janelle's score on the final exam, we need to substitute the score of the first test (xxx) into the linear regression equation.y^=11+0.5x\hat{y}=11+0.5xy^​=11+0.5x

STEP 3

Substitute x=90x = 90x=90 into the equation to calculate the predicted final-exam score.y^=11+0.5(90)\hat{y}=11+0.5(90)y^​=11+0.5(90)

STEP 4

Perform the multiplication.y^=11+45\hat{y}=11+45y^​=11+45

STEP 5

Add the values to find the predicted final-exam score.y^=11+45=56\hat{y}=11+45=56y^​=11+45=56The predicted value of Janelle's score on the final exam is 56.

STEP 6

To find the residual, we need to subtract the predicted final-exam score from the actual final-exam score.Residual=Actual score−Predicted scoreResidual = Actual\, score - Predicted\, scoreResidual=Actualscore−Predictedscore

STEP 7

Substitute the actual score (60) and the predicted score (56) into the formula to calculate the residual.Residual=60−56Residual = 60 - 56Residual=60−56

STEP 8

Calculate the residual.Residual=60−56=4Residual = 60 - 56 = 4Residual=60−56=4The value of the residual is 4.

Start learning now

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

Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

Assumptions
1. The linear regression equation is given by $\hat{y}=11+0.5x$ .
2. $\hat{y}$ is the predicted final-exam score.
3. $x$ is the score on the first test.
4. Janelle scored 90 on the first test.
5. The actual final-exam score for Janelle is 60.

To find the predicted value of Janelle's score on the final exam, we need to substitute the score of the first test ( $x$ ) into the linear regression equation.
$\hat{y}=11+0.5x$

Substitute $x = 90$ into the equation to calculate the predicted final-exam score.
$\hat{y}=11+0.5(90)$

Perform the multiplication.
$\hat{y}=11+45$

Add the values to find the predicted final-exam score.
$\hat{y}=11+45=56$
The predicted value of Janelle's score on the final exam is 56.

To find the residual, we need to subtract the predicted final-exam score from the actual final-exam score.
$Residual = Actual\, score - Predicted\, score$

Substitute the actual score (60) and the predicted score (56) into the formula to calculate the residual.
$Residual = 60 - 56$

Calculate the residual.
$Residual = 60 - 56 = 4$
The value of the residual is 4.