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.

W*hen you are predicting values it is a good idea to increase the domain
and range of the window beyond*

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 **r ^{2} = .580**. This

Also the **Coefficient of Non-determination** can be found by subtracting
**r ^{2 }**from

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
**