More Correlation Practice

Positive, Negative, or No Correlation?

No Correlation

Positive Correlation

Negative Correlation

Positive, Negative, or No Correlation?

4. Number of Homeless People vs. Crime Rate

5. Number of Storks in Denmark vs. the Number of children born

6. Age of Driver vs. Cost of Insurance

Positive Correlation

No Correlation

Negative Correlation

Put the following correlation values in order from weakest to strongest.

0.29, -0.87, -0.41, 0.03, -0.59, -0.92, 0.68

0.03, 0.29, -0.41, -0.59, 0.68, -0.87, -0.92

**Even though the #s are negative, the strong correlations are closer to 1**

Daily Check

Line of Best FitLinear Regression

A little vocab…• The line of best fit is the line that lies as close as

possible to all the data points.• Regression is a method used to find the equation

of the line of best fit.• Extrapolation is the use of the regression curve

to make predictions outside the domain of values of the independent variable.

• Interpolation is used to make predictions within the domain values of the independent variable.

Example 1:The environment club is interested in the relationship

between the number of canned beverages sold in the cafeteria and the number of cans that are recycled. The data they collected are listed in this chart.

a) Plot the points to make a scatter plot.

b) Use a straightedge to approximate the line of best fit by hand.

c) Find an equation of the line of best fit for the data.

# of Canned Drinks Sold

18 15 19 8 10 13 9 14

# of Cans Recycled 8 6 10 6 3 7 5 4

Example 1:

2 4 6 8 10 12 14 16 18 20

2

4

6

8

10

12

14

16

18

20

Entering Data : TI 36X - Pro

1. DATA DATA 4 (this will clear all the data)2. DATA (type in data)3. 2nd DATA4. LinReg ax + b (for linear regression) ExpReg ab^x (for exponential regression)

L1 L2 ONE YES CALC5. a = b = r = 6. The equation of the line is y = ax + b.7. Correlation Coefficient is r.

Example 2: The table shows the total outstanding consumer debt

(excluding home mortgages) in billions of dollars in selected years. (Data is from the Federal Reserve Bulletin.)

Let x = 0 correspond to 1985.

Year 1985

1990

1995

2000

2003

Consumer Debt 585 789 109

61693

1987

a) Find the regression equation appropriate for this data set. Round values to two decimal places. y 79.86x 463.35

L1 L2

0 585

5 789

10 1096

15 1693

18 1987

Example 2:

Year 1985

1990

1995

2000

2003

Consumer Debt 585 789 109

61693

1987

b) Find and interpret the slope of the regression equation in the context of the scenario.

79.86 represents the increase in consumer debt each year.

c) Find the approximate consumer debt in 1998.

$1501.52 billion

d) Find the approximate consumer debt in 2008.

$2300.13 billion

(y ax b is in table, year13)

(Already in table, year 23)

Example 3: The table below shows the number of deaths per

100,000 people from heart disease in selected years.

(Data is from the U.S. National Center for Health Statistics.)

Let x = 0 correspond to 1960. Year 1960 1970 1980 1990 2000 2002

Deaths

559 483 412 322 258 240

a) Find the regression equation appropriate for this data set. Round values to two decimal places. y 7.62x 559.25

x = 0 10 20 30 40 42

Example 3:

b) Find and interpret the slope of the regression equation in the context of the scenario.

-7.62 is the decrease in deaths caused by heart disease each year.

c) Find the approximate number of deaths due to heart disease in 1995. 293 deaths

d) Find the approximate number of deaths due to heart disease in 2008.

194 deaths

Year 1960 1970 1980 1990 2000 2002

Deaths

559 483 412 322 258 240

ClassworkLinear Regression