Illinois State University Mathematics Department
MAT 312: Probability and Statistics for Middle School Teachers Dr. Roger Day (day@ilstu.edu) 
Assignment #3: Possible Solutions 



Use the Couples' Ages data set, handed out in class, to complete the following tasks.
1. Create the equation for the medianmedian line of this data set, using husband's ages as the first element (x) of each ordered pair and wife's ages as the second element (y) in each ordered pair. Show all steps in the process as we illustrated in class and express your equation in slopeintercept form. You can check the equation of your medianmedian line using your calculator.
Here is the scatter plot of the data. Below it, I show each of the three clusters of data points from which we generate the summary points.



Using the outer summary points, the equation of the line containing them is
or, approximately,
When x = 31, this equation gives us y = 828/29, or approximately 28.5517.
Our second summary point, however, has a yvalue of 28, so we need to move our line onethird of the distance between y = 28 and y = 828/29. This distance is one third of 16/29, or 16/87, which is approximately 0.1839.
So we decrease the yintercept of our first line by 16/87, giving us the equation
or, approximately,
Your calculator can confirm for you the ordered pairs comprising the summary points and the equation of this medianmedian line. Here is the scatter plot of the data with the medianmedian line on it.
2. Use your calculator to generate the leastsquares linear regression equation for this data set, using husband's ages as the first element (x) of each ordered pair and wife's ages as the second element (y) in each ordered pair. Copy all the information your calculator shows you when you generate the leastsquares equation. Express your equation in slopeintercept form.
After entering the data into a TI83 calculator and selecting the command for Linear Regression, the calculator shows the following:
LinReg 
So the leastsquares linear regression equation is
Here is a scatter plot of the data with both regression lines on it. The red line is the medianmedian line and the green line is the leastsquares line.
3. Calculate the sum of the squared error terms (SSE) for each of the models you just created (i.e., for the medianmedian line and for the leastsquares line). You are encouraged to use your calculator's "lists" features to carry out your calculations. Express each sum rounded to the nearest hundredth of a unit.
The SSE for the medianmedian line is 617.95 and the SSE for the leastsquares line is 461.22. Look at the last plot above and convince yourself, graphically, why the SSE is smaller for the leastsquares line.
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