For Bob’s simple linear regression example, he wants to see how changes in the number of critical areas (the predictor variable) impact the dollar amount for land development (the response variable). If the value of the predictor variable (number of critical areas) increases, does the response (cost) tend to increase, decrease, or stay constant? For Bob, as the number of critical features increases, does the dollar amount increase, decrease or stay the same?
We test this by using the characteristics of the linear relationships, particularly the slope as defined above. Remember from hypothesis testing, we test the null hypothesis that a value is zero. We extend this principle to the slope, with a null hypothesis that the slope is equal to zero. Non-zero slopes indicate a significant impact of the predictor variable from the response variable, whereas zero slope indicates change in the predictor variable do not impact changes in the response.
Let’s take a closer look at the linear model producing our regression results.