Question

Marine biologists are interested in the physical characteristics of whales. The following least squares regression line model was fit to data on x = length (in feet) and y = jaw width (inches) for 20 whales found in various magazine articles. Researchers would like to test whether there exists a positive linear relationship between the two variables at the significance level 0.05. What is the correct testing result?

Term	Estimate	Std Error	t Ratio	Prob > |t|
Intercept	4.07	2.10	1.938	0.068
length	0.78	0.38	2.053	0.055

	a.	p-value is 0.055. We reject Ho so that  there exists a positive linear relationship between the two variables.
	b.	p-value is 0.068. We fail to reject Ho so that  there does not exist a positive linear relationship between the two variables.
	c.	p-value is 0.034. We reject Ho so that  there exists a positive linear relationship between the two variables.
	d.	p-value is 0.055. We fail to reject Ho so that  there does not exist a positive linear relationship between the two variables.
	e.	p-value is 0.0275. We reject Ho so that  there exists a positive linear relationship between the two variables.

Answer 1

We always take p-value of other than p-value of intercept.

Hence the required p-value is 0.055

This is more than 0.05 (alpha)

Hence, we fail to reject H0, and in regression analysis if we fail to reject null hypothesis then there doesn't exists a linear relationship.

So, Option D) p-value is 0.055. We fail to reject Ho so that  there does not exist a positive linear relationship between the two variables. is the answer.

I hope this will help. Thank you.