# AP Statistics : How to test of significance for the slope of a least-squares regression line

## Example Questions

### Example Question #1 : Mean And Linear Regression

A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.

False

True

True

Explanation:

A p-value of 0.1 is generally not sufficient to reject the null hypothesis, but this is only because we want a high degree of confidence before finding a relationship between variables.  Here, there is most likely a relationship between the variables even though the statistician could not reject the null hypothesis.

### Example Question #2 : Mean And Linear Regression

For a data set, the least-squares regression line has a confidence interval for the slope of .

Based on this confidence interval, what can you do with a hypothesis test at significance level where and ?

Fail to reject the null hypothesis because this confidence interval does not include .

Fail to reject the null hypothesis because this confidence interval does not include .

Not enough information to be able to decide.

Reject the null hypothesis because this confidence interval does not include .

Reject the null hypothesis because this confidence interval does not include .

Reject the null hypothesis because this confidence interval does not include .

Explanation:

Notice that the interval does not include . This means that the P-value for the hypothesis test would be under 5%, which would lead us to reject our null hypothesis.

Any confidence interval can be used to create a hypothesis test by inverting it, and it is fairly simple, but the concept is tested into graduate-level statistics theory.

### Example Question #3 : Mean And Linear Regression

Which of the following is an incorrect condition requirement for regression inference?

A trend/pattern of some sort in the residual plot

The standard deviation of the response must be constan

Ordered pairs must be independent of each other

A linear relationship between and Response must vary normally about the regression line for any given value of  