Introduction to Econometrics & Regression Basics Flashcards
What is econometrics
Econometrics is the use of statistical methods to analyze economic data. It helps answer “how much?” types of questions, such as:
How much does education impact wages?
How much does a tax increase affect economic growth?
What is the Simple Linear Regression Model (SLR)?
Y=β0+β1X+u
What is each component of the SLR?
Y= Dependent variable (the outcome we want to explain)
X = Independent variable (the factor we think influences Y)
β0 = Intercept (Value of Y when X=0)
β1 = Slope coefficient (measures the effect of X on Y)
u = error term (Captures everything effecting Y that isn’t in the model)
give the example of how education affects wage?
Wages (Y) = β0 + β1(years of education) + u
Analyse the education wage SLR?
if β1 = 2.5 this means that with each additional year of education wages increase by £2.50 per hour (on average)
What is Ordinary Least squares (OLS)?
it is the method we use to estimate the true values of β0 and β1.
It finds the line that best fits the data by minising the sum of squared residuals
What are residuals?
The differences between actual and predicted values of Y
What is the OLS forumal?
Min∑(Yi - Y^i)^2
Yi is the actual value and the other Yi is the predicted value
What does OLS produce?
it gives us the best linear unbiased estimator (BLUE) under certain assumptions
What are the 3 models to interpret Regression coefficients?
Level-Level Model
log-Level Model
Log-log model
What is the Level - Level Model?
Y=β0+β1X+u
a 1 unit increase in X leads to a β1 unit change in Y
Example of the Level-Level model?
Y=β0+β1X+u
If Y=wages and X = education and β1 = 2 then one more year of education increases wages by £2
What is the Log-Level model?
log(Y) = β0 + β1(X) + u
a 1% increase in X leads to a 100 x β1% change in Y
What is an example of the Log-Level Model?
log(Y) = β0 + β1(X) + u
if = 0.04 then one more year of education increases wages by 4%
What is the Log-Log model?
log(Y) = β0 + β1 log(X) + u
a 1% increase in X leads to a β1% in Y
what is an example of the Log-Log model?
log(Y) = β0 + β1 log(X) + u
if β1 = 0.8 then a 1% increase in education increases wages by 0.8%
What is R^2?
R^2 = 1 - SSR/SST
it is the coefficient of the determination and allows us to see how well a model explains Y after estimating it.
what are the different components that make up R^2?
SST (Total sum of squares) = Total variation in Y
SSR (sum of squared residuals) = unexplained variation
SSE (sum of squared explained variation) = variation explained by the model
SST = SEE + SSR
How can R^2 be interpreted?
if R^2 = 0.8 the model explains 80% of the variation in Y
if R^2 = 0.2 hte model only explains 20% of the variation of Y
A high 𝑅2 doesn’t always mean a good model! It could be misleading if the data has a trend or spurious correlation.
doesn’t indicate causation
What are the assumptions of OLS?
1) Linearity in parameters = model is correctly specified as linear
2) Random Sampling → Data points are randomly selected
3) No Perfect Collinearity → X must vary in the sample.
4) Zero Conditional Mean → E[u∣X]=0, meaning no omitted variable bias. ensures no bias
5) Homoskedasticity → The variance of errors is constant. if violated we have Heteroskedasticity which affects standard errors
