Handout on Understanding the Regression Line
In this discussion, we will look at the meaning of the slope and the y-intercept of the regression line.
A study was done to investigate the relationship between the age in years of a young person x and the time y in minutes at which the child can run one mile. Data from children between the ages of 8 and 15 was collected. The equation of the regression line was found to be
y = 17 - 0.5x
Interpret the slope and y-intercept.
The slope is -0.5. What this mean is that for every increase of 1 in x there is a decrease of 0.5 in y. In the context of the question, we can say that on average, as a child ages one year their time to run a mile goes down by 30 seconds (half a minute).
The y-intercept is 17, which means that when x is 0, y is 17. For this question, the y-intercept is not relevant, since 0 year old children cannot run one mile.
A biologist wants to study the relationship between the number of trees x per acre and the number of birds y per acre. She came up with the equation of the regression line
y = 5 + 4.2x
The slope is 4.2. This means that for every additional tree, you can expect an average of 4.2 additional birds per acre. The y-intercept 5 has meaning in this case. We can say that the average number of birds per acre in an area with no trees is 5.
For the following exercises, State what the slope and y-intercept are and interpret them if relevant. If not relevant, explain why.