Karteikarten
Simple linear regression model
Karten in diesem Stapel (30)
- 1In a simple linear regression model, what does y represent?dependent/explained/response/predicted variable or regressand
- 2In a simple linear regression model, what does x represent?independent/explanatory/control/predictor variable or covariate or regressor
- 3In a simple linear regression model, what does u represent?error/disturbance term
- 4If u is fixed, what is the effect of x on y?β1Δx
- 5What is the zero conditional mean assumption?The expected value of u does not depend on x.
In other words the expected value of the error term on x is equal to the expected value of the error term - 6What is the mathematical expression of ZCM?E(u|x) = E(u) = 0
- 7Why do we require β0 in our model?So it can be defined to make the assumptio E(u) = 0 true
- 8What is the effect of a ZCM violation?Would be estimating a correlation and not a causation
- 9What is the population regression function?Represents the true relationship between y and x
E(y|x) = β0 + β1x
This is an ideal which is never reached as ZCM does not hold and population data is difficult to gather - 10What is the sample regression function?y = β0 + β1x + u
The PRF plus the error encountered using a sample and a regression - 11Give a brief description of the Ordinary Least Squares (OLS) methodFitting a line through a cloud of observations
OLS chooses the line that minimises the sum of square residuals.
The corrosponding values for the equation of that line makes the OLS estimators - 12Give the fitted values equationanswer on a physical flashcard
- 13What is the residual for observation i?answer on a physical flashcard
- 14How do you calculate the sum of square residuals? Why is it used?answer on a physical flashcard
- 15Why do we use the sum of square residuals?- minimising residuals without squaring means residuals can be positive or negative
- to make all residuals as negative as possible is to pick a fitted line which indefinitely high up
-minimising absolute value of residuals results in no closed form solution (theory more complicated)
- BLUE (best linear unbiased estimator)
- simplest but most efficient - 16What are the 3 properties of OLS estimation?answer on a physical flashcard
- 17How do you calculate total sum of squares? Why is it used?answer on a physical flashcard
- 18How do you calculate explained sum of squares? Why is it used?answer on a physical flashcard
- 19Why is R2 used?Captures fraction of sample variation in y explained by x
Ratio between what the model can measure and the total variation - 20What type of values do we want for R2?as close to 1 as possible
- 21What is the difference between the error term and residual?- Error term is in population parameters equation and is unobservable
- Residual is in estimated equation = estimated error on each value of i
- ZCM involves error term not residuals so can never be verified (need to use reasoning and theory) - 22Under what assumption is the OLS unbiased?1. population model is linearin parameter with an error term
2. random sample: x and y are independent and identically distributed, error terms are independent across observations
3. some sample variation: xs are not all the sample value
4. ZCM: E(u|x) = 0 - 23What happens if any of the assumption don't hold?The regression is biased and not a good representation of the true relationship between x and y
1. ways to model non-linear functins as linear
2. problem in time-series as value at t may be correlated with values at t-1, t+1 etc
3. cannot calculate OLS without it
4. If x and u are correlated then a spurious correlation is being estimated rather than a causation (relationship is really due to unobserved factors in u that influence y but are also correlated with x) - 24What does variance calculate?On average how much each observation varys from the mean (expected value)
- 25What additional assumption related to variance is required? What are all the assumptions collectively known as?5. the error term does not change over the values of x
This assumption is not required for OLS unbiasedness
Gauss-Markov assumptions - 26How do you calculate variance of the intercept term?On formula sheet
- 27How do you calculate the variance of the slope coefficient?On formula sheet
- 28How do you estimate the error variance?On formula sheet
- 29How do you calculate the se of the slope coefficient?answer on a physical flashcard
- 30What happens if the intercept term does not equal 0 and it is omitted from the model?OLS estimator of β1 will be biased
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- Year 2 ECN21004 - Econometrics Karteikarten am Simple linear regression model, erstellt von Imogen Donoghue am 11/01/2023.
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- Imogen Donoghue
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