In a large statistics class, students have taken two exams. For each of the foll

Question

In a large statistics class, students have taken two exams. For each of the following situations, report what you would expect for the value of the correlation coefficient between exam 1 score and exam 2 score. Give a brief justification for your answer.

1. Every student scores ten points higher on exam 2 than on exam 1.

2. Every student scores half as many points on exam 2 than on exam 1.

3. Every student guesses randomly on every question on both exams.

4. Every student scores twenty points less on exam 2 than on exam 1.

5. Every student scores 180 points for his/her combined score on the two exams.

Explanation / Answer

if we have a linear function of one on the 2nd then the correlation coefficient = 1

1) as the marks are perfect linear to paper 1 hence the correlation = 1

2) again there is a linear relation between paper 1 and two therefore coefficient = 1

3) in this there is no linear relation between the two hence we can not get the correlation 1 therefore correlation will be gretaer then 0 but less then 1

4) here as the 20 marks above shows a linear relation that two perfect hence it will be a perfect correlation =1

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