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Regression and Prediction Answer the following questions from the Coladarci (2011) text: Chapter 8: Exercises 2, 6, 12, 16, 17. I also need to answer the following questions from the Coladarci (2011) text:

Chapter 11: Exercises 8, 9, 13, 14, 17, 18, 20

Chapter 12: Exercises 4, 5, 7, 10

Chapter 13: Exercises 2, 4, 5, 7, 9, 13, 19

2. The relationship between student performance on a state-mandated test administered

in the fourth grade and again in the eighth grade has been analyzed for a large group

of students in the state. Ellen obtains a score of 540 on the fourth-grade test. From

this, her performance on the eighth-grade test is predicted (using the regression line)

to be 550.

(a) In what sense can the value 550 be considered an estimated mean?

(b) Why is it an estimated rather than an actual mean?

6. Following are the scores on a teacher certiﬁcation test administered prior to hiring (X) and the principal’s ratings of teacher effectiveness after three months on the job (Y) for a group of six ﬁrst-year teachers (A–F):

A B C D E F

Test score (X): 14 24 21 38 34 49

Principal rating (Y): 7 4 10 8 13 11

(a) Compute the summary statistics required for determining the regression equation for predicting principal ratings from teacher certiﬁcation test scores.

(b) Using values from Problem 6a calculate the intercept and slope; state the regression equation.

(c) Suppose that three teachers apply for positions in this school, obtaining scores of 18, 32, and 42, respectively, on the teacher certiﬁcation test. Compute their predicted ratings of teacher effectiveness.

(d) If in fact these data were real, what objections would you have to using the equation from Problem 6b for prediction in a real-life situation?

12. (No calculations are necessary for this problem.) Suppose the following summary statistics are obtained from a large group of individuals: X ¼ 52:0, SX ¼ 8:7, Y ¼ 147:3,

SY ¼ 16:9. Dorothy receives an X score of 52. What is her predicted Y score if:

(a) r = 0?

(b) r = [1].55?

(c) r = +.38?

(d) r = [1]1.00?

(e) State the principle that emerges from your answers to Problems 12a to 12d.

(f) Show how Formula (8.5) illustrates this principle.

16. At the end of Section 8.3, we asked you to consider how the location of Student 26 would affect the placement of the regression line in Figure 8.4.

(a) Imagine you deleted this case, recalculated intercept and slope, and drew in the new regression line. Where do you think the new line would lie relative to the original regression line? Why? (Refer to the least-squares criterion.)

(b) How should the removal of Student 26 affect the magnitude of the intercept? The slope?

(c) With Student 26 removed, the relevant summary statistics are X ¼ 69:45,

SX ¼ 9:68, Y ¼ 100:83, SY ¼ 14:38, r ¼ :79. Calculate the new intercept and slope.

(d) As accurately as possible, draw in the new regression line using the ﬁgure below

(from which Student 26 has been deleted). How does the result compare with your response to Problems 16a and 16b?

17. At the end of the section on “setting up the margin of error," we asked if you can see from Table A in Appendix C how we got “1.00" and “2.58" for 68% and 99% conﬁdence, respectively. Can you?

Regression and Prediction Answer the following questions from the Coladarci (2011) text: Chapter 8: Exercises 2, 6, 12, 16, 17. I also need to answer the following questions from the Coladarci (2011) text:

Chapter 11: Exercises 8, 9, 13, 14, 17, 18, 20

Chapter 12: Exercises 4, 5, 7, 10

Chapter 13: Exercises 2, 4, 5, 7, 9, 13, 19

2. The relationship between student performance on a state-mandated test administered

in the fourth grade and again in the eighth grade has been analyzed for a large group

of students in the state. Ellen obtains a score of 540 on the fourth-grade test. From

this, her performance on the eighth-grade test is predicted (using the regression line)

to be 550.

(a) In what sense can the value 550 be considered an estimated mean?

(b) Why is it an estimated rather than an actual mean?

6. Following are the scores on a teacher certiﬁcation test administered prior to hiring (X) and the principal’s ratings of teacher effectiveness after three months on the job (Y) for a group of six ﬁrst-year teachers (A–F):

A B C D E F

Test score (X): 14 24 21 38 34 49

Principal rating (Y): 7 4 10 8 13 11

(a) Compute the summary statistics required for determining the regression equation for predicting principal ratings from teacher certiﬁcation test scores.

(b) Using values from Problem 6a calculate the intercept and slope; state the regression equation.

(c) Suppose that three teachers apply for positions in this school, obtaining scores of 18, 32, and 42, respectively, on the teacher certiﬁcation test. Compute their predicted ratings of teacher effectiveness.

(d) If in fact these data were real, what objections would you have to using the equation from Problem 6b for prediction in a real-life situation?

12. (No calculations are necessary for this problem.) Suppose the following summary statistics are obtained from a large group of individuals: X ¼ 52:0, SX ¼ 8:7, Y ¼ 147:3,

SY ¼ 16:9. Dorothy receives an X score of 52. What is her predicted Y score if:

(a) r = 0?

(b) r = [1].55?

(c) r = +.38?

(d) r = [1]1.00?

(e) State the principle that emerges from your answers to Problems 12a to 12d.

(f) Show how Formula (8.5) illustrates this principle.

16. At the end of Section 8.3, we asked you to consider how the location of Student 26 would affect the placement of the regression line in Figure 8.4.

(a) Imagine you deleted this case, recalculated intercept and slope, and drew in the new regression line. Where do you think the new line would lie relative to the original regression line? Why? (Refer to the least-squares criterion.)

(b) How should the removal of Student 26 affect the magnitude of the intercept? The slope?

(c) With Student 26 removed, the relevant summary statistics are X ¼ 69:45,

SX ¼ 9:68, Y ¼ 100:83, SY ¼ 14:38, r ¼ :79. Calculate the new intercept and slope.

(d) As accurately as possible, draw in the new regression line using the ﬁgure below

(from which Student 26 has been deleted). How does the result compare with your response to Problems 16a and 16b?

17. At the end of the section on “setting up the margin of error," we asked if you can see from Table A in Appendix C how we got “1.00" and “2.58" for 68% and 99% conﬁdence, respectively. Can you?

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