# roblem Set 9.1

Problem Set 9.1

1. Suppose you have 50 data points and you calculate the sample correlation coefficient and find that r=.29. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

2. Suppose you have 10 data points and you calculate the sample correlation coefficient and find that r=.61. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

3. Suppose you have 28 data points and you calculate the sample correlation coefficient and find that r=-.44. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

4. Suppose you have 17 data points and you calculate the sample correlation coefficient and find that r=.54. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

5. Suppose you have 45 data points and you calculate the sample correlation coefficient and find that r=-.23. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

6. Suppose you have 34 data points and you calculate the sample correlation coefficient and find that r=.32. Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify your answer.

7. By hand compute the sample correlation coefficient for the following data:

x 2 3 7 10 15

y 1 8 9 11 12

Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify you answer.

8. By hand compute the sample correlation coefficient for the following data:

x 1 2 4 7 10

y 5 8 10 15 19

Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify you answer.

9. By hand compute the sample correlation coefficient for the following data:

x 1 3 4 9 10

y 20 18 10 8 4

Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify you answer.

10. By hand compute the sample correlation coefficient for the following data:

x 3 6 8 10 15

y 5 2 10 7 1

Can you be 95% confident that a linear relation exists between the variables? If so, is the relation positive or negative? Justify you answer.

# Problem Set 9.2

Problem Set 9.2

1. Find the best fit line for the following data:

x 2 3 7 10 15

y 1 8 9 11 12

(Notice that this is the same data as in problem 7 from problem set 9.1. You may use any calculations that you did for that problem to help you with this problem.)

2. Find the best fit line for the following data:

x 1 2 4 7 10

y 5 8 10 15 19

(Notice that this is the same data as in problem 8 from problem set 9.1. You may use any calculations that you did for that problem to help you with this problem.)

3. Find the best fit line for the following data:

x 1 3 4 9 10

y 20 18 10 8 4

(Notice that this is the same data as in problem 9 from problem set 9.1. You may use any calculations that you did for that problem to help you with this problem.)