PS 225Lecture 17

Correlation

Line Review

Scatterplot (Scattergram)

X: Independent Variable Y: Dependent Variable Plot X,Y Pairs

Length (in) Weight (oz)

18 22

19 26

22 25

23 23

20 22

19 21

Relationships

Relationships

Relationships

General Linear Relationship

Correlation Coefficient

R Measure of the strength of a linear relationship Sign denotes the direction of the relationship Absolute value denotes the strength of the

relationship Close to 1, strong Close to zero, weak

What if the mean of a variable is dependent on the value of another variable? Is it dependent? How much is it dependent? How can we express the dependence algebraically?

Scatterplots with Positively Correlated Data

As x increases, y increases The correlation coefficient, r, is positive

Scatterplots with Negatively Correlated Data

As x increases, y decreases The correlation coefficient, r, is negative

Scatterplots with Non-Linearly Correlated Data

Values of r

R is between -1 and 1 -1 is negatively correlated 1 is positively correlated 0 is not correlated

Hypothesis

Ho: No linear relationship between x and y variables

Ha: There is a linear relationship between x and y variables

Scatterplot Age Wed vs. # of Children

SPSS Correlation

Definition

r2

Coefficient of determinationis the proportion of the variation in y thatis explained by the linear relationship.

Measuring Correlation with SPSS Output

Adding Regression Line

Equation for a Line

y=mx+b M is slope

“rise over run” Ratio of increase in y-coordinate and

increase in x-coordinate B is y-intercept

Value of y where the line crosses the y-axis

X has a value of zero at that point

Example

Label the x and y axis Graph the point (2,2) Graph the line y = 2x + 1

If x is 3, what is the value of y?

SPSS Assignment

Does the number of years of education an individual has affect the hours of television a person watches?

Does age affect the hours of television a person watches?

How might the above relationships impact the results of Putnam’s study?