Correlations and Line of Fit

Students will explore the line of fit/correlations of data sets without having to create a scatterplot.

Explanatory/Response Variables For the following variables, please decide if they are random

variables or explanatory/response, and if they are explanatory/response…decide which one is which.

A family’s income and the years of education their eldest child completes.

Your pay and the type of job you have.

Your IQ test score and your school GPA

The age you start crawling and when you stopped eating baby food.

Correlation What is a brief definition of correlation?

Draw a scatterplot that would have a correlation of exactly 1.

Draw a scatterplot that would have a correlation of exactly -1.

Draw a scatterplot that has a correlation of 0.

Draw a scatterplot that has a correlation of -0.7 and another at 0.5

Line of fit Instead of calling the line of fit, the line of fit, we are going to

call the regression line.

The regression line helps us predict what will happen in the future.

We can use our calculator to find it.

Y = a + bx where b is the slope and a is the y-intercept.

Practice finding the regression line

Age x in months

Height y in centimeters

18 76

19 77

20 78

21 78

22 79

23 80

24 80

25 81

26 81

27 82

28 83

29 84

Use your calculator to find the regression line.

Predict the height of someone at 32 months.

Predict the height of someone at 240 months.

If someone is 90 centimeters, how old are they?

What does it mean? Explain what the slope and y-intercept means to each

problem in the real world.

SAT math score = 572 – 1.04 x percent taking the test

Pay at your job = 100 + 1.75 x years on the job

Weight of soap = 54 – 2.38 x days