QA7 - Linear Regression

Question 1

Describe the models that can be estimated using linear regression and differentiate from those which can not

Answer 1

For linear regression to be applicable:
1. explanatory variables are linear in unknown coefficients
2. error must be additive
3. explanatory variables must be observable

Question 1

Describe the key assumptions of OLS parameter estimation

Answer 1

1. error has mean zero
2. data are realisations from iid random variables
3. variance of data greater than zero
4. variance of error is constant
5. no outliers in the data

Question 2

Construct, apply, and interpret hypothesis tests and confidence intervals for a single regression coefficient in a regression

Answer 2

s = sqrt((1/n-2) * sum(errors ^2))

For B:
T = (bhat - b0) / (s / sqrt(sum (xi - bxar)^2)) ~ N(alpha)

For a:
T = (ahat - a0) / ((s^2 * (1/n) * sum(xi^2)) / sum((xi - xbar)^2)) ~N(alpha)