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Number of offspring and weight, in pounds, of 23 randomly selected rabbits are compared. Which significance test should be used to see if number of offspring and weight have a linear relationship? Assume all test conditions are met. (4 points)

User KillerFish
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1 Answer

1 vote

Answer:

t test for the slope of regression line

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.

User My Alter Ego
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