Question

Running a linear regression produces the following : hat y =37.5-12.75x

r = - 0.72

r ^ 2 = 0.52

SE slope =2.85

n = 29

a) Is this a positive or negative correlation? How do you know?

b) Without running the t-tests, does this appear to be a strong correlation?

c) Based on the test statistic t = (slope)/(SESlope) can we claim there is correlation?

Answer 1

Regression equation is

where slope = -12.75 and intercept = 37.5

a)

Correlation coefficient = r = -0.72 which is negative.

This is negative correlation.

b)

Values between 0.7 and 1.0 (−0.7 and −1.0) indicate a strong positive (negative) linear relationship through a firm linear rule.

r = -0.72

So we can say that this is a strong negative correlation.

c)

Null hypothesis :

Alternative hypothesis :

where is population slope

Test statistic:

t = -4.474 (Round to 3 decimal)

n = 29

Degrees of freedom = n - 2 = 29 - 2 = 27

t critical value for = 0.05 and df = 27 is

tc = 2.052 (From excel using function, =TINV(0.05,27))

Here |t| = 4.474 > tc =2.052

So we reject H0.

Conclusion: There is correlation.