Ch2: Woolridge: The Simple Regression Model

Question 1

What is the simple regression model used for?

Answer 1

To study the relationship between two variables

Question 2

What does the simple regression model study?

Answer 2

the two variables x and y. it studies how y varies with changes in x. example: y is a community crime rate and x is number of police officers.

Question 3

What is the equation for the simple regression model?

Answer 3

y = b0 + b1x + u

Question 4

What are the different names for the Y variable?

Answer 4

dependent variable
explained variable
response variable
predicted variable
regressand

Question 5

What are the different names for the X variable?

Answer 5

Independent variable
Explanatory variable
Control variable
Predictor variable
Regressor
Covariate

Question 6

What is u?

Answer 6

The error term or disturbance in the relationship. It represents factors other than x that affects y. the model treats all of those factors as being unobserved. so think of u as unobserved

Question 7

What is b1?

Answer 7

the slope parameter

Question 8

What is b0?

Answer 8

the intercept parameter, aka constant term

Question 9

What is the natural measure of the association between two random variables?

Answer 9

the correlation coefficient

Question 10

What happens if u and x are uncorrelated?

Answer 10

there will not be linearly related

Question 11

What is the assumptions of the ordinary least squares?

Answer 11

Assumptions of OLS:
- Linearity: The relationship between X and Y is linear.
- Independence: Observations are independent of each other.
- Homoscedasticity: Variance of errors is constant across all levels of X and Y.
- Normality: Errors are normally distributed (important for inference).

Question 12

What is the residual?

Answer 12

The difference between the actual value and its fitted value. (actual - estimated) y - yhat

Question 13

What is the sum and the sample average of the OLS residuals?

Answer 13

zero

Question 14

What is the sample covariance between the regressors and the OLS residuals?

Answer 14

zero

Question 15

What is the total sum of squares (SST)?

Answer 15

Total candies (SST): All the candies in the jar, including the ones you guessed right and wrong.

Question 16

What is the explained sum of squares (SSE)? (aka sum of squares residuals)

Answer 16

Residual candies (SSR): These are the candies that you didn’t guess right. So, SSR is like the mistake or the difference between how many candies you thought there were and how many there actually were. It’s the part your guess didn’t get right!

Question 17

What is the explained sum of squares (SSE)?

Answer 17

Explained candies (SSE): The candies that your guess got right—those are the ones you were able to predict correctly.

Question 18

What R-squared of the regression? (sometimes called the coefficient of determination) (goodness-of-fit)

Answer 18

R^2 = SSE/SST = 1 - SSR/SST

R-squared is like a score that tells you how well your guesses match the actual number of candies.

If R-squared is 1, it means your guesses are perfect—there’s no difference between what you guessed and what was actually in the jar.

If R-squared is 0, it means your guesses are really far from the truth, and they don’t help explain anything about the candies.

Question 19

What is the constant elasticity model?

Answer 19

The constant elasticity model is a way to describe how one thing (like price) affects another thing (like quantity) in a consistent way, no matter how big or small the values are.

Imagine you’re selling candies, and you notice that every time you change the price, the amount of candies sold changes in a consistent percentage.

In a constant elasticity model:
- Elasticity tells us how much one thing changes in percentage when another thing changes by 1%.
- Constant means the percentage change stays the same no matter what.

For example, if the price of candies goes up by 10%, the quantity sold might go down by 5%. If that 5% decrease happens every time you increase the price by 10%, then the elasticity is constant.

In simple terms, the constant elasticity model says, “If I change one thing by a certain percentage, another thing changes by a fixed percentage every time.”

Question 20

What is the zero conditional mean?

Answer 20

The zero conditional mean is a rule in econometrics that says the average of the error terms (the “mistakes” in the model, u, the residual) should be zero when you have certain conditions.

Imagine you’re guessing how many candies are in a jar based on some clues. The error is how far your guess is from the actual number of candies. The zero conditional mean means that, on average, your guesses will be correct (you don’t systematically overestimate or underestimate).

In more technical terms, it means that the average value of the errors should be zero when the values of the predictors (like the size of the jar or the color of the candies) are known. This is important because it ensures that your model doesn’t have bias and that your guesses are fair.

Question 21

What is homoskedasticity?

Answer 21

this assumption says that the variance of the unobservable, u, conditional on x, is constant. aka constant variance assumption.

Homoskedasticity means that the mistakes you make in your predictions are spread out evenly for all values of your predictor.

Imagine you’re guessing how many candies are in a jar based on the size of the jar: If your mistakes are small for both small and large jars, and they look about the same for every jar size, that’s homoskedasticity.

homoskedasticity just means that your mistakes are consistent no matter what size jar (x) you’re looking at!

Question 22

What is heteroskadasicity?

Answer 22

if your mistakes are bigger for large jars and smaller for small jars, that’s heteroskedasticity, which means the spread of the mistakes changes with the size of the jar.

Question 23

What is the difference between errors and residuals?

Answer 23

Errors are unknown and represent the true mistakes.

Residuals are what we actually calculate based on our model’s predictions, acting as estimates of the errors.

Question 24

What is the binary variable? (aka dummy variable)

Answer 24

can take two variables: 0 and 1

Question 25

What does squared error explain?

Answer 25

How much of the total variation is not described by the regression line?

Question 26

What is the coefficient of determination? (also called r squared) (khan)

Answer 26

tells what % of total variation is described by the line (the variation in x). tells us how good of a fit the line is in the plot relative to observer points!

Question 27

What is the exogeneity of covariates?

Answer 27

The exogeneity of covariates means that the independent variables (or predictors) in a regression model are not related to the error term. It’s a key assumption in econometrics that ensures your model gives reliable and unbiased estimates of the coefficients.