INTRODUCTION TO ECONOMETRICS
UPDATED ACTUAL QUESTIONS AND
CORRECT ANSWERS COMPLETE STUDY
GUIDE FULL SOLUTION
●● What is the simple regression model?
Answer: It's a model that explains the relationship between two variables
using a straight line.
●● What is the equation for the simple regression model?
Answer: Equation is: y = β₀ + β₁x + u
y = dependent variable (explained variable, response variable, predicted
variable, regressand)
x = independent variable (explanatory variable, control variable,
predictor variable, regressor)
β₀ = intercept
β₁ = slope (effect of x on y)
u = error term (captures other factors).
●● What does β₁ (the slope) mean?
Answer: β₁ shows how much y changes when x increases by 1 unit,
keeping all other factors constant. (This is technically only true when
,both the zero mean of error assumption and zero conditional mean
assumptions are held)
●● What does β₀ (the intercept) mean?
Answer: It's the predicted value of y when x = 0.
●● What is the error term (u)?
Answer: It represents all other factors that affect y but are not included
in the model/equation.
●● What is meant by "ceteris paribis"?
Answer: Holding other factors fixed -It means we pretend nothing else
changes except x when we study how x affects y.
●● What does the assumption E(u) = 0 mean?
Answer: It means on average, the error term (u) is zero—so, the
unobserved factors don't systematically affect y in one direction (Some
above and some below)
●● What does "linearity" mean in the context of simple linear
regression?
Answer: Linearity means y changes by the same amount when x
increases by one unit, no matter the starting value of x.
,●● Why is linearity often unrealistic in real life?
Answer: Because in reality, effects can change depending on levels of x
(for example, another year of education might have smaller benefits after
many years of schooling).
●● What is the "zero conditional mean assumption"?
Answer: It says the average value of u doesn't depend on x, written as
E(u|x) = 0.
●● Why is E(u|x) = 0 important?
Answer: Because it ensures that x and the error terms are uncorrelated,
allowing us to estimate β₀ and β₁ accurately/with reduced bias
●● What happens when E(u|x) ≠ 0?
Answer: Then x is correlated with u, meaning there's omitted variable
bias, and our β estimates are unreliable.
●● What is the population regression function (PRF)?
Answer: It shows the average (expected) value of y for each x, written as
E(y|x) = β₀ + β₁x.
●● What is the Sample Regression Function (SRF)?
Answer: It's the line we actually estimate with data: ŷ = b₀ + b₁x ("y-hat"
is the predicted y).
, ●● How do we estimate β₀ and β₁ from data?
Answer: How do we estimate β₀ and β₁ from data?
●● How do we estimate β₀ and β₁ from data?
Answer: We use Ordinary Least Squares (OLS) estimation.
●● What does OLS do?
Answer: OLS finds the line that minimizes the sum of squared
differences (errors) between the actual y values and the predicted y
values. (So minimising the square of the average distance between the
actual values and the line of best fit)
●● What are "residuals"?
Answer: Residuals (êᵢ or ûᵢ) are the differences between actual y and
predicted ŷ.
●● Why do we square the residuals?
Answer: Squaring makes all differences positive and gives more weight
to larger errors, helping find the best-fitting line.
●● What are the formulas for OLS estimates?
Answer: Slope: b₁ = Σ(xᵢ − x̄)(yᵢ − ȳ) / Σ(xᵢ − x̄)²
UPDATED ACTUAL QUESTIONS AND
CORRECT ANSWERS COMPLETE STUDY
GUIDE FULL SOLUTION
●● What is the simple regression model?
Answer: It's a model that explains the relationship between two variables
using a straight line.
●● What is the equation for the simple regression model?
Answer: Equation is: y = β₀ + β₁x + u
y = dependent variable (explained variable, response variable, predicted
variable, regressand)
x = independent variable (explanatory variable, control variable,
predictor variable, regressor)
β₀ = intercept
β₁ = slope (effect of x on y)
u = error term (captures other factors).
●● What does β₁ (the slope) mean?
Answer: β₁ shows how much y changes when x increases by 1 unit,
keeping all other factors constant. (This is technically only true when
,both the zero mean of error assumption and zero conditional mean
assumptions are held)
●● What does β₀ (the intercept) mean?
Answer: It's the predicted value of y when x = 0.
●● What is the error term (u)?
Answer: It represents all other factors that affect y but are not included
in the model/equation.
●● What is meant by "ceteris paribis"?
Answer: Holding other factors fixed -It means we pretend nothing else
changes except x when we study how x affects y.
●● What does the assumption E(u) = 0 mean?
Answer: It means on average, the error term (u) is zero—so, the
unobserved factors don't systematically affect y in one direction (Some
above and some below)
●● What does "linearity" mean in the context of simple linear
regression?
Answer: Linearity means y changes by the same amount when x
increases by one unit, no matter the starting value of x.
,●● Why is linearity often unrealistic in real life?
Answer: Because in reality, effects can change depending on levels of x
(for example, another year of education might have smaller benefits after
many years of schooling).
●● What is the "zero conditional mean assumption"?
Answer: It says the average value of u doesn't depend on x, written as
E(u|x) = 0.
●● Why is E(u|x) = 0 important?
Answer: Because it ensures that x and the error terms are uncorrelated,
allowing us to estimate β₀ and β₁ accurately/with reduced bias
●● What happens when E(u|x) ≠ 0?
Answer: Then x is correlated with u, meaning there's omitted variable
bias, and our β estimates are unreliable.
●● What is the population regression function (PRF)?
Answer: It shows the average (expected) value of y for each x, written as
E(y|x) = β₀ + β₁x.
●● What is the Sample Regression Function (SRF)?
Answer: It's the line we actually estimate with data: ŷ = b₀ + b₁x ("y-hat"
is the predicted y).
, ●● How do we estimate β₀ and β₁ from data?
Answer: How do we estimate β₀ and β₁ from data?
●● How do we estimate β₀ and β₁ from data?
Answer: We use Ordinary Least Squares (OLS) estimation.
●● What does OLS do?
Answer: OLS finds the line that minimizes the sum of squared
differences (errors) between the actual y values and the predicted y
values. (So minimising the square of the average distance between the
actual values and the line of best fit)
●● What are "residuals"?
Answer: Residuals (êᵢ or ûᵢ) are the differences between actual y and
predicted ŷ.
●● Why do we square the residuals?
Answer: Squaring makes all differences positive and gives more weight
to larger errors, helping find the best-fitting line.
●● What are the formulas for OLS estimates?
Answer: Slope: b₁ = Σ(xᵢ − x̄)(yᵢ − ȳ) / Σ(xᵢ − x̄)²
