Topic 11- Extensions To Regression Analysis

Question 1

This topic looks at alternate ways to specify a regression model. E.g non-linear

Question 2

4 types of new variables in regression equations

Answer 2

Natural logarithms of variables
Quadratic variables
Interaction variables
Dummy variables

Question 3

Natural logarithm 2 uses

Answer 3

Condenses the dataset, make a non-linear relationship into a linear.

Can also make a skewed distribution become more normally distributed.

Question 4

X values for natural logarithm (on the graph)

Answer 4

X=1 on the graph is a 0 log value
X<1 is a negative log value
X>1 is a positive log value

(Line looks roughly like the beginning of a laffer curve)

Question 5

How to use logarithms in regression. (In words)

Answer 5

Assume a non-linear relationship between independent variable (x) and dependent variables (y), but a linear relationship between lnX and lnY

Question 6

Logarithm regression equation

Answer 6

LnY=a+blnX+e

Where
B=r(SlnY/SlnX)
A=lnY bar - blnX bar

(Basically just add ln to each X and Y from the basic regression formula)

Question 7

2: Quadratic variables

Answer 7

Analyse relationships with a quadratic shape e.g tax (laffer curve)

Question 8

Example: estimating happiness with age

What would the regression equation look like, and also in general

Answer 8

Happiness=a+b₁AGE+b₂AGE²+e

General
Y=a+b₁x₁+b₂x²₁+b₃x₂+…+e

Question 9

How to find the minimum/maximum

Answer 9

Differentiate to find turning point

Question 10

Draw out the 4 quadratic variable grpahs

Question 11

Interaction variables, and example

Answer 11

2 independent variables have an additional impact on y (THE DEPENDENT) if they BOTH OCCUR

E.g stirring coffee, and adding sugar.
Sweetness will not be impacted by just sugar or just stirring

It will be affected by sugar and stirring.

Question 12

Example: if testing if it is young or unemployed people, or young AND unemployed people that cause high crime

What would the regression equation look like

Answer 12

Crime=a+b₁YOUNG+b₂UNEMPLOYED+b₃YOUNG x UNEMPLOYED+e

Question 13

Final new type of variable: Dummy variables purpose

Answer 13

Allows us to include nominal scale data or qualitative variables into the regression model e.g gender, unemployed or employed.

Take value of 0-1

E.g 1=female 0=men
0 usually means attribute not present

Question 14

Example: we want to find out effect of gender on wages

What would the regression equation look like?

Answer 14

WAGE=a+b₁EDUCATION+b₂GENDER+b₃CHILDREN+b₄MARRIED+e

Here we can see we added gender, and included control variables to isolate the effect of gender on wages.

Question 15

Using the example equation, how do we interpret the b₂ coefficient?

Answer 15

Let gender
1=female
0=male

If b₂>0, women earn more
If b<0 women earn less

Question 16

Note: we can interact dummy variables too

E.g b₅GENDER x CHILDREN

Question 17

Aside: P value in ,,

Answer 17

=p=0.1
**=p=0.05
**=p=0.01 (highest confidence as smallest)