Regression


The paired data below consist of the total weights (in pounds) of discarded garbage and the sizes of households.

Total weight    10.8    19.9    27.6    38.1    27.9    21.9    21.8    49.3    33.3    35.5


Size                  2          3        3          6        4          2         1         5         6         4

Draw a Scatter Plot, Give the regression equation, Predict the family size if 32 pounds of garbage is discarded, and predict the pounds of discarded garbage for a household of size 8. On the calculator we begin by entering data into the Lists.

Press (this screen will appear)



You should enter your X-values into LIST1 and the Y-values into LIST2.



To see a Scatter Plot we go to STAT PLOT. Press

(see upper left screen)

Press Next make sure "ON" is highlighted and press

Arrow down and highlight Scatter Plot (see upper right screen)

Make sure Xlist : L1, Ylist : L2 you may choose any "mark" you desire

Next we must adjust the WINDOW to fit the data so press

(you will see the screen on the top left of page 59) OR you may choose


Match your settings to screen above.

Now press (see screen above)

We see there appears to be a positive correlation.

When you are predicting values it is a good idea to increase the domain and range of the window beyond the actual data. This is still necessary even when you are using "ZOOM 9 "

Now to determine the regression equation we go to the Statistical Calculations Menu so press ( lower left screen will appear)


Arrow right to "CALC" and down to 4 : LinReg (aX+b) (see above)


Press (lower left screen will appear)

Since the default setting will use LIST1 and LIST2 we can now press

As you can see from the screen the regression equation is Y = .119X + .183

We also see the correlation coefficient r = .762, and one other piece of information r2 = .580. This “r2 is called the Coefficient of Determination. It is the ratio of the explained variation to the amount of total variation.

Also the Coefficient of Non-determination can be found by subtracting r2 from 1.000 . It is: 1.000 - 0.580 = 0.420

You may be wondering just how closely this best fit line matches our data. We can graph the regression line on top of our data by following these several steps:


First press (this screen will appear)

Now press (you will see this screen)

Arrow down to 5 : Statistics... and press (see screen below)


Arrow right and highlight "EQ". "1 : RegEQ" should also be highlighted.
Press (this screen will appear)


As you can see the regression equation has been pasted into the function line.

Now press (the regression equation will be graphed along with the original data)


You can find the predicted values from this screen. We want to find the size of a family if 32 lbs of garbage was discarded. Now we go to the Function Calculations Menu.

Press TRACE

 

"1 : value" should be highlighted then press (this screen will appear)

 

We simply enter the value and press (this screen will appear)



As you can see from the screen we would predict a family of size 4 .

Lastly, we want to find the pounds of garbage discarded if the family size is 8. Since we know "Y" (lbs of garbage) we need to enter that information into the function line (Y=).

So press Arrow down to Y2=

Enter

Next press (this screen will appear)



The intersection point is our solution.

Again press
Arrow down to 5 : intersect and press (see below left)

Notice that at the top of the screen the regression equation is displayed


Press ( see above right screen)



Press again (see above left)

Press one more time (you will see the screen above right)

As you can see the intersection point is X=65.4, Y= 8, so for our problem the predicted amount of garbage from a family of 8 would be 65.4 lbs