Answer:
t test for the slope of regression line
Step-by-step explanation:
Suppose a random sample is drawn from the bivariate normal population and the estimated regression equation is found Y^= a +bX , where, b , the sample estimate of β1 is normally distributed with mean β and standard deviation
σyx / √∑(x-x`)².
The test statistic has t distribution where
t= b-β/sb
where sb= Syx / √∑(x-x`)² with υ= n-2 degrees of freedom.
It is important to note that the testing of hypothesis that β= 0 is equivalent to testing the hypothesis that variable Y is independent of the variable X in the linear sense.
The test statistic then becomes t= b/ sb .
If we reject H0 : β= 0 we conclude that the two variables are linearly independent.
