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.