Question

Use the following to answer 1 - 6.

Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are given below.

Test A 64 48 51 59 60 43 41 42 35 50 45

Test B 91 68 80 92 91 67 65 67 56 78 71

What is the value of the linear coefficient r?

.567

.974

.863

.488

Question 2

Assuming a 0.05 level of significance, what is the critical value?

.602

.576

.666

.632

Question 3

What do you conclude about the correlation of the variables?

There is significant negative linear correlation between the variables.

There is no significant linear correlation between the variables.

There is insufficient information to make a conclusion about the linear correlation between the variables.

There is significant positive lnear correlation between the variables.

Question 4

What is the slope of the regression line?

-6.84

6.84

1.32

-1.32

Question 5

What is the y-intercept of the regression line?

-10.59

-12.27

12.27

10.59

Question 6

What is the percent of explained variation determined by the regression line?

32.1%

23.8%

74.2%

95.0%

Question 7

Which of the following could not represent a correlation coefficient?

1.004

.926

.371

-0.986

Answer 1

1)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.974

2)

critical value = .602

3)

There is significant negative linear correlation between the variables.

4)

slope=                      β̂1           =

Sxy/Sxx=

1.32

5)

intercept=              β̂0           =

y̅-β1x̅=

10.59

6)

Coeffficient of determination R^2 =r^2*100 =

95.0%

7)

1.004 (since r can be between -1 and 1)