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?