Lecture 5 - MLR A Flashcards
Describe the MLR model. 2 points
1) Involves several independent variables
2) Linear relationship between y and each x
MLR uses the least squares method true or false?
true
What does each coefficient give in the MLR model?
bi gives the average change in y for a one unit change in xi when all other explanatory variables are held constant
What are the five assumptions of the MLR model?
1) There is a linear relationship between y and each x
2) The error terms have equal variance
3) The error terms are independent
4) The error terms are normally distributed
5) The independent variables must not be correlated with each other.
What are the 2 implications of the MLR assumption that the error terms are normally distributed?
1) The expected value (avg.) of error terms is zero
2) y values are normally distributed for each x
What is the implication of the MLR assumption of constant variance of errors?
The error variance is constant for all x (homoscedasticity)
What is the implication of the independence of errors assumption of the MLR model?
The amount of error at a given x should be unrelated to that at other x values.
What is the F test used for in relation to the MLR?
Whether a relationship exists between the y and the x’s.
What are the null and alternative hypotheses for an F test of MLR variable relationships?
H0: beta 1 = beta 2 = … beta k = 0
H1: At least 1 beta not equal to zero
What does the t test show in relation to MLR?
It identifies which variables contribute to the relationship.
What is R squared called for MLR?
The coefficient of multiple determination
What does the coefficient of multiple determination indicate?
The percentage variation in y that is explained by the regression.
What does the adjusted R squared take into account that the regular coefficient of multiple determination does not?
The number of variables and the sample size.
How is the adjusted R squared used?
When comparing two or more models with different numbers of independent variables but the same dependent variable, choose the model with the HIGHER R squared value.
How is the confidence interval of a regression slope calculated?
Coefficient plue or minus t stat times the deviation related to the chosen coefficient.
