12.15.14 Lines of Best Fit and Correlation Coefficients

[Pages:4]Scatterplots, Lines of Best Fit, and Correlation Coefficients

Shoe Size vs. Height

Someone claims that there is a stron g

relationship between someone's height and their shoe sizes.

You are to investigate this claim.

So that males and females can be considered together, either subtract 1.5 from the women's shoe sizes or add 1.5 to the men's shoe sizes.

Is this

true?

1.

After graphing and viewing the scatterplot, do height and shoe size appear to be related? How?

2.

What is the line of best fit?

3.

What is the slope?

What does it mean?

4.

What is the y--intercept?

What does it mean?

Does it make sense?

5.

My sister's shoe size is 6.5.

What's her predicted

height?

Correlation Coefficient or r--value

The correlation coefficient, denoted r, is the measure of how well a collection of data points can be modeled by a line.

Correlation coefficients range between --1 and 1. The closer the correlation coefficient is to 1 or --1, the less scattered the

points are and the stronger the relationship. Only data points on the scatter plot which are a perfectly straight line can

have r = ?1 or r = 1.

--1

0

1

Line with a negative

No line fits because

Line with a positive

slope fits best

no pattern exists

slope fits best

Perfect Negative Correlation

No Correlation

Perfect Positive

Correlation

There are three different kinds of correlations:

1. Negative Correlation

2. No Correlation

3. Positive Correlation

When x increases, y

decreases. Points can be

approximated by a line

with negative slope.

There is no obvious

pattern or trend.

What an example of a situation that always has...

A negative correlation?

No correlation?

When x increases, y

increases.

Points can be

approximated by a line

with positive slope.

A positive correlation?

Using the Calculator

Step 1: Enter Data into Calculator 1. Press STAT, then select Edit, and press Enter.

2. Clear the list for L1 and L2 by selecting L1 and pressing clear, then selecting L2 and pressing clear. 3. Enter the x--values (total fat) in List 1. 4. Enter the y--values (total calories) in List 2.

Step 2: Viewing the Scatterplot

1. Press 2nd, Y=,

turn on the StatPlot1. 2. Go to Zoom9 ZoomStat

Step 3:

Find Line of Best Fit (in the calculator) When using the calculator to find the line of best fit, we are looking for the linear regression, which is just another name for line of best fit. 1. Once the data is entered in the lists, press STAT, then press over to CALC, then move down to 4, which is

LinReg(ax+b).

2. Press enter once to select LinReg(ax+b), then again for the calculator to actually compute the linear regression.

3. The screen that shows up will tell you the values of a and b, where a = m = slope and b = y--intercept. Write down

4. the equation of the line. y = ____________________________ 5. The vaule for r = correlation coefficient will also be shown. Remember, the closer r is to ? 1, the more accurate

the line of best fit is. (If r not showing up tell them to press 2nd 0, CATALOG, and scroll down to DiagnoticOn and press enter twice.)

Step 4: Transfering the Best Fit Line to Y1 1. Go to Y= and make sure Y1 is cleared. 2. Press VARS, then move down to 5, which is Statistics, press enter, then move over two to EQ, down to 1, RegEQ, and press enter to make RegEQ the equation in Y1. This is the equation you were given before.

Step 5:

Predict! 1. What is the predicted number of calories in hotdog that has 18 grams of total fat?

(Use table!)

_________ 2. Approximately, what is the total fat in grams of a sandwich that has 350 g of total calories? _________

Practice

A biologist is studying the relationship between a tree's diameter and its height. She records the following data for 7 different trees.

1.)

Find the line of best fit to model the data.

2.)

What is the slope?

What is the y--intercept?

3.)

What is the r--value?

What does it mean?

4.)

What is the predicted height of a tree that has a diameter 5.5 in.?

5.)

Find the predicted diameter of a tree that is 25 ft. tall.

Correlation Coefficient & Linear of Best Fit HW Name:

_____________

8. Predict the type (positive, negative, no) and strength of correlation (strong, weak) for the following pairs of quantities.

a. temperature and time for a cup of coffee left on the counter. b. temperature and time for a pot of cold water placed on a hot stove to boil. c. math test score and height d. amount of money in the bank and the number of days since the last paycheck.

9.

10.

11.

12.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download