Topic 10- Multiple Regressions

Question 1

Multiple regression model

Answer 1

Shows several independent variables to influence y (dependent variable)

Question 2

Multiple regression equation

Answer 2

Y=a+b₁x1+b₂x₂+b₃x₃+…+e

b are regression coefficients
A=y intercept
Independent variables are x

Question 3

Multiple regression test statistic

Answer 3

Ti=bi-β
/
se(b)

~T(n-j)

Same as normal regression test statistic, except the i’s added, and crit value found by (n-j), not (n-2)

Question 4

Method 2: confidence intervals

Answer 4

Same as regression before, if 0 doesn’t lie within the interval, we can reject null.

Question 5

Method 3: pvalue

Answer 5

P value less than significance level, we can reject.

Question 6

Regression hypothesises

Answer 6

Null: no significant effect/influence on y
Alternate: x has a significant influence on y

Question 7

How do we check the significance of the whole model?

Answer 7

F test from anova.

If F is high, it means at least something in model is significant in helping to predict the dependent variable

Question 8

Why use multiple regresssions (3)

Answer 8

Isolates individual effect of each variable

Control variables exclude wrong explanations for relationships between the variable of interest and Y.

Ceteris paribus- allows us to hold other things constant while testing for variable of interest

Question 9

Note: if we find a positive relationship between food expenditure and age. We don’t know why, it could be due to income, family size, and health.

To check if age is actually significant and a relationship exists between it and food expenditure, age should still be significant when the other variables are included