Introduction to Multiple Regression Flashcards
Idea of the multiple regression model
Examine the linear relationship between
1 dependent (Y) & 2 or more independent variables (Xi).
Coefficients of the multiple regression model
The coefficients of the multiple regression model are estimated using sample data
Why we need Adjusted r^2
r2 never decreases when a new X variable is added to the model.
This can be a disadvantage when comparing models.
What is the net effect of adding a new variable?
We lose a degree of freedom when a new X variable is added.
Did the new X variable add enough explanatory power to offset the loss of one degree of freedom?
Adjusted r^2
Shows the proportion of variation in Y explained by all X variables adjusted for the number of X variables used.
Penalises excessive use of unimportant independent variables.
Smaller than r2
Useful in comparing among models.
F Test for Overall Significance of the Model:
Shows if there is a linear relationship between all of the X variables considered together and Y.
multiple regression assumptions
The errors are normally distributed.
Errors have a constant variance.
The model errors are independent.
Are individual variables significant
Shows if there is a linear relationship between the variable Xj and Y.
Using dummy variables
A dummy variable is a categorical explanatory variable with two levels:
yes or no, on or off, male or female
coded as 0 or 1
Regression intercepts are different if the variable is significant.
Assumes equal slopes for other variables.
If more than two levels, the number of dummy variables needed is number of levels minus 1.
Interaction Between Independent Variables
interaction between pairs of X variables:
Response to one X variable may vary at different levels of another X variable.
Contains two-way cross-product terms:
Multiple regression model
1
Multiple regression sample equation
2-3
Pie sales example
4-7
rsquared
8-9
adjusted rsquared
10-11
Is the model significant (F test)
12-15
