14.4: Testing the Significance of the Slope and y-intercept Flashcards
What is the purpose of testing the significance of the slope in simple linear regression?
The significance test for the slope is performed to determine if there is a significant relationship between the predictor variable (x) and the response variable (y).
It helps in understanding whether changes in x are associated with changes in y.
What are the null and alternative hypotheses for testing the slope in simple linear regression?
The null hypothesis (H₀) is that the slope coefficient (β₁) equals 0 (H₀: β₁ = 0), implying no relationship between x and y. The alternative hypothesis (Hₐ) is that the slope coefficient (β₁) is not equal to 0 (Hₐ: β₁ ≠ 0), indicating a relationship does exist.
How is the test statistic for the slope significance calculated in simple linear regression?
What is the formula for the standard error of the slope estimate in simple linear regression?
How many degrees of freedom are used in the t distribution for the test statistic in simple linear regression?
What are the critical value and p-value rules for testing the significance of the slope in simple linear regression?
What does it mean if the slope is significant at the 0.05 or 0.01 significance levels?
If the slope is significant at the 0.05 level, there’s strong evidence that x is related to y.
If the slope is significant at the 0.01 level, it is considered very strong evidence of a significant regression relationship.
When might you use a one-tailed test instead of a two-tailed test for slope significance?
A one-tailed test may be used when there is a specific direction of interest (e.g., testing if β₁ > 0).
However, the two-tailed test is more common and is used to test the general significance of the slope (whether β₁ is different from 0 in either direction).
What is an F test in the context of simple linear regression, and when do you use it?
How do you decide to reject the null hypothesis using an F test in simple linear regression?
How are the critical value and p-value related in an F test?
How are the t statistic for the slope and the F statistic for the regression model related?
