Question

In regression analysis, the F test will provide the same conclusion as the t test if​

Question options:

	​there is only one dependent variable
	​there is only one independent variable
	​there is a positive correlation between x and y
	​the y-intercept is positive

Answer 1

In case of simple linear regression t-test and F-test both provide the same results.

To understand this , let us consider a simple linear regression model

The tests are used to conduct hypothesis tests on the regression coefficients obtained in simple linear regression.

The test statistic used for this test is:

The F ratio that underlies the analysis of variance test is the square of this,

The p-value for the t-test is the probability of recording a t-value as far from zero, and this equals the probability of getting as large an F-ratio as the one evaluated from the data.

Answer : there is only one independent variable (i.e. simple linear regression)