What is correlation?
A statistical measure describing the degree to which two variables change together. It indicates both strength and direction of a relationship.
What does the direction of a correlation tell us?
It shows whether variables move together in the same direction (positive correlation) or in opposite directions (negative correlation).
What does a scatter diagram show?
A visual display of the relationship between two variables where each point represents a pair of scores.
Is saying that something is correlated the same as saying one variable causes another? Why?
No. Correlation only shows that variables are related, not that one causes the other. The relationship could be coincidental or influenced by other variables.
Does a correlation coefficient of 0 necessarily mean that two variables are not correlated?
No. A coefficient of 0 means there is no linear relationship, but a curvilinear relationship may still exist.
What is the difference between a linear and curvilinear correlation, as shown in a scatter diagram?
Linear correlation forms a straight-line pattern, while curvilinear correlation forms a curved pattern.
What is the general rule for the degree of the relationship between two variables expressed by a correlation coefficient?
The closer the absolute value of r is to 1, the stronger the relationship. The closer it is to 0, the weaker the relationship.
How does a correlation coefficient improve our understanding of a relationship beyond what is shown in a scatter diagram?
It provides a precise numerical measure of both the strength and direction of the relationship.
Why are Z scores used to calculate a linear regression between two variables?
Z scores standardize variables so they share the same scale, allowing direct comparison and simplifying calculation of relationships.
What are the three possible explanations for a relationship between two variables?
1) A causes B
2) B causes A
3) A third variable influences both A and B
What is regression used for?
Regression is used to predict the value of one variable based on the value of another variable.
What is the formula for the prediction model using Z scores?
Zy’ = rZx
What are the steps for making predictions using raw scores?
1) Convert raw X to Zx
2) Multiply Zx by r to get Zy’
3) Convert Zy’ to raw Y using mean and standard deviation
What do r2 and R2 tell us?
They indicate the proportion of variance in one variable that is explained by its relationship with the other variable.
