Lecture 6: Predictive Data Analysis

Question 1

Before doing regression analysis, we can use a ? -graph plot to determine if the two variables have any linear relationship.

Answer 1

Before doing regression analysis, we can use a scatter-graph plot to determine if the two variables have any linear relationship.

Question 2

Ordinary Least Squares (OLS):
Minimise the ?? to find the best fit line.

With assumptions, OLS provides the ? (?), ?, ? Estimates (BLUE) of the model parameters (e.g. the betas)

Answer 2

Ordinary Least Squares (OLS):
Minimise the error variance to find the best fit line.

With assumptions, OLS provides the Best (consistent), Linear, Unbiased Estimates (BLUE) of the model parameters (e.g. the betas)

Question 3

Assumptions of OLS:

1. ?
2. E(ε) = ?
3. ? / Exogeneity: E(ε|X) = ?
4. No measurement errors in X
5. Homoskedasticity: Var(ε) = ?
6. No ?: cov( ε_i, ε_j) = ?

Answer 3

Assumptions of OLS:

1. linearity
2. E(ε) = 0
3. Independence/ Exogeneity: E(ε|X) = 0
4. No measurement errors in X
5. Homoskedasticity: Var(ε) = σ^2
6. No autocorrelation: cov( ε_i, ε_j) = 0

Question 4

OLS Method:
Minimise ????
Equation?

Answer 4

OLS Method:
Minimise sum of squared deviations:
Equation: https://images.app.goo.gl/ZeCmejWxkk7Jqb8r6

Question 5

OLS Method:
How to minimise sum of squared deviations?
Taking ?? and setting them to ?.

Answer 5

OLS Method:
How to minimise sum of squared deviations: Taking partial derivatives and setting them to 0.
https://images.app.goo.gl/Va4P582A3fDjFB3A9

Question 6

To check model fit, use ??? (i.e. ?-?):
proportion of change in ? that can be explained by change in ?
? <= R-squared <= ?

Answer 6

To check model fit, use Coefficient of Determination (i.e. R-squared):
proportion of change in Y that can be explained by change in X
0 <= R-squared <= 1 (100%)

Question 7

To test parameters’ significance, use ? testing & ?statistics:
Significance if ?? > critical value

Answer 7

To test parameters’ significance, use hypothesis testing & t statistics:
Significance if t-value > critical value

Question 8

Panel Data: ?? data (e.g. industries, firms,…) + ?-series data

Answer 8

Panel Data: cross-sectional data (e.g. industries, firms,…) + time-series data