Correlation & Regression Flashcards
Correlation
A correlation exists between two variables (eg 2 random variables X and Y) if one of them is related to the other in some way.
Correlation values
> 0 if X and Y both increase
Correlation does not imply what? Why?
Cause-effect relationship, because of the possible existence of a lurking variable.
Regression model
A regression model is a mathematical equation that describes the relationship between 2 or more variables.
Simple Regression
2 variables
Multiple regression
More than 2 variables
The 2 variables in a simple regression
Independent and dependent variables
Dependent variable
the one being explained
Independent variable
The one used to explain the dependent variable.
Linear regression
A regression that gives a straight-line r elationship between 2 variables.
We use which method to get the best-fitting line?
Method of least squares
Method of least squares
We minimize the sum of squares of the distance between the observed values and predicted values for y or x.
Always want regression line to do what?
Go through (xbar, ybar)»_space;> ybar = b0+b1 * xbar
Sign of b1 depends on
Sxy
We cannot use the slope b1 to predict the strength of the relationship because…
it is affected by units.
Solution to problem of units
We use a standardized slope, the (Pearson) Linear Correlation Coefficient
r has the same sign as…
b1
interpreting r
the closer r is to plus or minus 1, the stronger the linear relationship
r>0
positive linear correlation
r
negative linear correlation
r stays the same even if you do what?
change units of x and y or change the role of x and y
No significant linear correlation equals
nothing. Does not mean that there is no relation at all
When to use the regression line to make predictions
When there is a significant linear correlation
Both r and r^2 do what? How are they different?
They both measure the strength of the linear association, but have different interpretations.
