Confidence Intervals and Significance Tests for Correlation and Regression (4 of 5)

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This will always be the case: The test of the null hypothesis that the correlation is zero is the same as the test of the null hypothesis that the regression slope is zero.

Assumptions

1. Normality of residuals: The errors of prediction (Y-Y') are normally distributed.
   
   
2. Homoscedasticity
   
   
3. The relationship between X and Y is linear.
   
   

Summary of Computations: Significance test for r

1. Compute r
   
   
2. Compute t using the formula:
   
   
   
   with N-2 degrees of freedom where N is the number of pairs of scores.