Chapter 14 Notes:
Inference for the Regression Model:

 

Step 1: Make a scatterplot

 

Step 2: Calculate the LSRL

Step 3: Identify outliers and influential points

 

Step 4: Calculate the correlation (r value)

 

 

 

Assumptions for Regression Inference:

1. The y responses vary according to a normal distribution.

2. The y responses are independent of each other.

3. The true relationship is linear.

4. The standard deviation s about the true regression line is constant.

 

 

 

The true regression line is written in the form: where a is the true x-intercept and b is the true slope.

 

Since s is unknown, we use s to estimate the value of s.

 

Note: (n 2) is the degrees of freedom for the regression model.

 

 

 

A level C confidence interval for the slope b of the true regression line is .

 

 

 

To test whether or not there is a correlation between two quantitative variables, consider the slope of the regression line. If there is no correlation, the slope would be zero.

H0: b = 0

 

To test this hypothesis, compute the t statistic and P-value.