PS 225 Lecture 17 Correlation Line Review

Scatterplot (Scattergram)  X: Independent Variable  Y: Dependent Variable  Plot X,Y Pairs Length (in)Weight (oz)

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 r2r2 Coefficient of determination is the proportion of the variation in y that is 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?