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. Example 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.   Solution 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.   Example 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.   Exercises For the following exercises, State what the slope and y-intercept are and interpret them if relevant.  If not relevant, explain why. A psychologist has collected data on the number of times x per year a college student goes out on a date and the number of hours y of homework that student does per week.  She came up with the equation of the regression line     y  =  30 - 0.2x   A police chief wants to investigate the relationship between the number y of times a person has been convicted of a crime and the number of criminals x that person knows.  The equation was found to be     y  =  0.4 + 8x   A doctor is researching the relationship between the number of packs of cigarettes per day x a person smokes and the number of days per year y the person is sick.  The doctor comes up with the equation of the regression line     y  =  6 + 1.2x   A snowboard wholesaler wants to investigate the number y of customers that came to each rental shop each year x.  The equation of the regression line is     y  =  -999,000 + 50x   A study was done to look at the number y of a certain type of fossil based on the distance x in meters from a water source.  The equation of the regression line is     y  =  24 - 1.4x