Question

In the table below, let X be the number delinquent peers a respondent has and Y be the number of arrests they have.  Calculate the bivariate correlation between X and Y and provide an interpretation of the correlation coefficient documenting whether it is significant.

X	Y
2	1
3	1
3	3
5	3
6	3
6	5
7	6
8	8
8	9
10	9

Using the data, calculate the equation for an ordinary least squares regression (slope, Y-intercept, and r²).  Interpret each of these 3 values.

Answer 1

Run a regression analysis in excel followed by below procedures:

1. Go to data tab --> data analysis --> choose Regression

Regression Summary output:

Least square regression equation y = -1.681 + 1.117 x

Slope = 1.117

Y-intercept = -1.681

Correlation coefficeint r = 0.932 (it is strong positive linear relationship)

Conclusion:

P-value = 0.0000840

P-value is less than the significance level.

If the p-value is less than the significance level (α=0.05):

• Decision: Reject the null hypothesis.
• Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero."