Linear Regression on the Calculator

Please view this tutorial and answer the follow-up questions on loose leaf to

turn in to your teacher.

What is Linear Regression?

• Linear regression is also known as “line of best fit”

• You can estimate it by hand using a scatterplot and a ruler

• You can get the exact line of best fit by using the LinReg function on your calculator

Steps for Finding Linear Regression on the Calculator

1. Enter your information in a list2. Quit your lists3. Find the linear regression line by going to STAT

then CALC then 8:LinReg(a+bx) then hit ENTER4. Tell your calculator where the information is (Ex.

L1, L2)5. Hit ENTER and plug in your values for a and b

(Round values for a and b to 2 decimal places.)

Example

Income in 1988

Income in 1994

$77,900 $121,200

$102,000 $174,900

$155,000 $255,200

$76,200 $126,200

$124,300 $200,400

The table to the left gives the average income for different medical specialties for 1988 and 1994.

Example

Income in 1988

Income in 1994

$77,900 $121,200

$102,000 $174,900

$155,000 $255,200

$76,200 $126,200

$124,300 $200,400

First, you’ll need to enter your information

into a list.

Put the Income in 1988 in L1 and the Income in

1994 in L2 then quit your lists.

Example

Next, you need to hit STAT then go over to

CALC.

Then go down to 8:LinReg(a+bx) and hit

ENTER.

Example

You’ll see this screen.

You need to tell the calculator where your information is. In this

case, the x information is in L1 and the y

information is L2.

Example

Hit 2nd 1 then Comma (above the 7)

then 2nd 2.

Hit ENTER. You’ll see the values for a and b.

Example

Now all you need to do to find your line of best fit is plug in your values

for a and b to the general equation for

the line.

Don’t forget to round values for a and b to TWO decimal places!

Examplea = -2525.06b = 1.66

So the equation of the line is:

y=−2525.06 +1.66x

Since the general form of the equation is

y = a + bx, a is your y-interecept and b is your

slope.

Example

y=−2525.06 +1.66x

How can we check that this line is a

good fit?

Make a scatterplot of the information on the calculator then graph

the y= equation.

Example

y=−2525.06 +1.66x

Check to see if the line touches some points, has some

points above it and some points below it. This line is a great fit!

Example

Once you have your line of best fit, you can use it to make

estimations.

For example, our problem was talking

about income in 1988 versus the income in

1994.

If you earned $120,000 in 1988, how much could you expect to earn in 1994?

Example

Type your equation in y= then find $120,000

in your x column by changing your

TblStart to 120,000.

If you made $120,000 in 1988, you can expect to earn $196,675 in 1994.

Follow-Up Questions

Answer the following questions on loose leafand hand them in to your teacher.

Follow-Up Questions

Here are the prices for different Nintendo game systems when they were first released. Answer the following questions based

on this information.

Game System

Year Price

NES 1985 $200

Super Nintendo

1991 $249

Nintendo 64

1996 $199

Game Cube 2001 $225

Wii 2006 $250

Follow-Up Questions

NOTE: When entering the years in your list, change them to YEARS SINCE 1985.

For example, 1991 would be entered as 6 since it is 6 years since 1985.

Game System

Year Price

NES 1985 $200

Super Nintendo

1991 $249

Nintendo 64

1996 $199

Game Cube 2001 $225

Wii 2006 $250

Follow-Up QuestionsGame

SystemYear Price

NES 1985 $200

Super Nintendo

1991 $249

Nintendo 64

1996 $199

Game Cube 2001 $225

Wii 2006 $250

1. Write the linear regression line for the Nintendo information.

2. What is the slope? What is the y-intercept?

3. Using your linear regression line, estimate the price of a new system if it were released in 2011.

4. In what year will the price of a newly released system by $277?