# Standard Error in Estimates

The following is a list of grade levels and ages for 15 students:

Age Grade

16 10

15 9

15 10

14 8

12 6

11 5

11 6

10 4

9 3

9 4

8 2

7 2

6 1

6 2

5 1

Compute the regression equation predicting grade level from age and using that equation, determine the predicted grade level for a 13-year-old student. Then calculate the standard error of estimate for the prediction in the part above and using that value, determine to the nearest tenth the two grade levels between which we can be 95% confident that a 13-year-old student will be. Next calculate the coefficient of determination and coefficient of non-determination for the relationship between age ans grade. Explain what each of these values tells us. Lastly, compute the regression equation prdicting age level from grade and using that equation, determine the predicted age for a 9th grader.

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#### Solution Preview

Please refer to the attachment.

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<br>Compute the regression equation predicting grade level from age and using that equation, determine the predicted grade level for a 13-year-old student.

<br>

<br>The formula of coefficients of Y=a+bX+e is:

<br>b=Σ[(X-Xm)(Y-Ym)] /Σ[(X-Xm)^2] = 0.875

<br>a=Ym-b*Xm= -4.115

<br>where Xm is mean of Age, and Ym is mean of Grade.

<br>so the regression is

<br>Grade = - 4.115+0.875 Age

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<br>When Age = 13

<br>Grade = - 4.115+0.875*13 = 7.26

<br>

<br>Then calculate the standard error of estimate ...

#### Solution Summary

Compute regression equation, predict grade level, calculate standard error of estimate, and calculate coefficient of determination and non-determination.

The following is a list of grade levels and ages for 15 students:

Age Grade

16 10

15 9

15 10

14 8

12 6

11 5

11 6

10 4

9 3

9 4

8 2

7 2

6 1

6 2

5 1

Compute the regression equation predicting grade level from age and using that equation, determine the predicted grade level for a 13-year-old student. Then calculate the standard error of estimate for the prediction in the part above and using that value, determine to the nearest tenth the two grade levels between which we can be 95% confident that a 13-year-old student will be. Next calculate the coefficient of determination and coefficient of non-determination for the relationship between age ans grade. Explain what each of these values tells us. Lastly, compute the regression equation prdicting age level from grade and using that equation, determine the predicted age for a 9th grader.