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Question 2 [About Regression analysis: 11 marks] A research was made of the midterm and final scores in a large course, with the following results: average midterm score = 60, SD = 15 average final score = 50, SD = 20, $r = 0.60$ The scatter diagram was football-shaped. For each student, the midterm score was predicted from the final score using regression line. Please use the above information to answer question #2-1 to question #2-5: 2-1. (1 mark) Predict the midterm score for a student whose final score was unknown. A) 15 B) 20 C) 50 D) 60. 2-2. (1 mark) Predict the midterm score for a student whose final score was 30. A) 35 B) 43 C) 51 D) None of the above. 2-3. (1 mark) The above prediction is likely to be off by ______ points or so. A) 6 B) 9 C) 10 D) 12. 2-4. (2 marks) About what percentage of students score below 75 on the midterm A) 92% B) 88% C) 86% D) 84%. 2-5. (2 marks) Of the students who scored 70 on the final, about what percentage of students score below 75 on the midterm? A) 82% B) 78% C) 69% D) None of the above.

          Question 2 [About Regression analysis: 11 marks] A research was made of the midterm and final scores in a large course, with the following results:
average midterm score = 60, SD = 15
average final score = 50, SD = 20, $r = 0.60$
The scatter diagram was football-shaped. For each student, the midterm score was predicted from the final score using regression line. Please use the above information to answer question #2-1 to question #2-5:
2-1. (1 mark) Predict the midterm score for a student whose final score was unknown.
A) 15 B) 20 C) 50 D) 60.
2-2. (1 mark) Predict the midterm score for a student whose final score was 30.
A) 35 B) 43 C) 51 D) None of the above.
2-3. (1 mark) The above prediction is likely to be off by ______ points or so.
A) 6 B) 9 C) 10 D) 12.
2-4. (2 marks) About what percentage of students score below 75 on the midterm
A) 92% B) 88% C) 86% D) 84%.
2-5. (2 marks) Of the students who scored 70 on the final, about what percentage of students score below 75 on the midterm?
A) 82% B) 78% C) 69% D) None of the above.

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Question 2 [About Regression analysis: 11 marks] A research was made of the midterm and final scores in a large course, with the following results:
average midterm score = 60, SD = 15
average final score = 50, SD = 20, r = 0.60
The scatter diagram was football-shaped. For each student, the midterm score was predicted from the final score using regression line. Please use the above information to answer question #2-1 to question #2-5:
2-1. (1 mark) Predict the midterm score for a student whose final score was unknown.
A) 15 B) 20 C) 50 D) 60.
2-2. (1 mark) Predict the midterm score for a student whose final score was 30.
A) 35 B) 43 C) 51 D) None of the above.
2-3. (1 mark) The above prediction is likely to be off by points or so.
A) 6 B) 9 C) 10 D) 12.
2-4. (2 marks) About what percentage of students score below 75 on the midterm
A) 92% B) 88% C) 86% D) 84%.
2-5. (2 marks) Of the students who scored 70 on the final, about what percentage of students score below 75 on the midterm?
A) 82% B) 78% C) 69% D) None of the above.

Added by Amy S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

11/30/2023

Step 1

The regression line equation is: Midterm score = a + b(final score) where a is the intercept and b is the slope. Show more…

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Question 2 /Absent Regression analysis: A research was made of the midterm and final scores in a finance course, with the following results: average midterm score - 60, SD = 15 average final score - 30.5, SD = 20, r = 0.60 The scatter diagram was football-shaped. For each student, the midterm score was predicted from the final score using a regression line. Please use the above information to answer questions 2.1 to 2.5: 2.1. (1 mark) Predict the midterm score for a student whose final score was unknown. A) 15 B) 20 C) 50 D) 60 2.2. (1 mark) Predict the midterm score for a student whose final score was 30. A) 35 B) 43 C) 51 D) None of the above. 2.3. (1 mark) The above prediction is likely to be off by q points or so. A) 6 B) 9 C) 10 D) 12 2.4. (2 marks) About what percentage of students score below 75 on the midterm? A) 92% B) 88% C) 86% D) 84% 2.5. (2 marks) Of the students who scored 70 on the final, about what percentage of students score below 75 on the midterm? A) 82% B) 78% C) 69% D) None of the above. $2.1 to question 2.5 A) 15 20 30 50 60 A) 35 43 51 None of the above A) 6 9 10 12 A) 92% 88% 86% 84% A) 82% 78% 69% None of the above

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Transcript

00:01 So we have a linear regression line for the final and then 10 plus .9 times the midterm.

00:10 And a, if susan scored 70 on the midterm, we want to predict what she would get on the final.

00:21 So we are going to plug that in place of the midterm grade.

00:24 So 10 plus .9 times 70 gives us a value of 73.

00:32 Part b asks us, if susan got an 80 on the final, how big would her residual be? so her point was the point 70 and 80.

00:45 So her residual would be the 80 minus the predicted 73.

00:52 So it would be 7.

00:54 Part c, if the standard deviation of the finals was 12 points and the standard deviation of the midterm, so the standard deviation of the final is equal to, if the standard deviation of the final is 12 points and the standard deviation of the midterm is 10 points, what is the correlation? well, the correlation is equal to the slope times the standard deviation of y over the standard deviation of x.

01:29 So the slope will be .9 times the standard deviation of the y, which is going to be your final, over the standard deviation of the x.

01:43 So we have .9 times basically 1 .2.

01:47 And that comes out to be incorrect.

01:54 And you see my problem, don't you? i switched these because obviously we cannot have those values.

02:03 And the formula that i missed, the slope is equal to r times the standard deviation of y over the standard deviation of x.

02:11 Therefore, this r is equal to the standard deviation of x divided by the standard deviation of y.

02:16 So i left this in here and didn't redo the video because that should be a 10 and that should be a 12.

02:21 And so .9 times and then 10 divided by 12 gives us a correlation coefficient of .75.

02:29 I knew something was wrong when i got a value larger than 1.

02:33 So left that in there just so you can see sometimes we mess up.

02:38 Letter d says, how many points would a person need to score to have a predicted value of 100 on the final? so 100 is equal to that 10 plus .9 times the midterm...

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