INTRODUCTION TO REGRESSION ANALYSIS
QUESTIONS WITH CORRECT ANSWERS 2025
Regression model is concerned with... (2) - correct answers-modelling the relationship between two or
More variables.
We make regression models to see whether models variables have anything to do with each other
2. Bivariate linear regression model can be written as (1)
Explain each variable (5)
Examples (3) - correct answers-x is the independent or explanatory variable
Y is the dependent or explained variable
U is a random error or disturbance
Α and β are parameters which characterise the relationship between
Y and x. The parameters are not observable directly.
Α - intercept
Β - slope
Examples: income and spending(?), wage and gender,(?) Student high
and exam scores(?)
Two interpretations of the regression mode - correct answers-1. The x values are chosen by the
investigator e.g. By a process of experimentation.
(in this case the x variable is not random and can be treated as being 'fixed in repeated samples')
2. The x and y variables are jointly distributed random variables with cov(x,y) ≠ 0
(this is more realistic for economic data but harder to deal with when deriving the distribution of
estimators)
, 5. What do we try to find out from the linear regression model - correct answers-try to estimate pop
parameters
Y and x are available
What is the problem with the system, (linear regression model)
And what is the solution - correct answers-problem is that system is over-determined - we have more
equations than unknown variables.
Mayer's (1750) solution. Form linear combination of equations to reduce number of equations to
number of unknown coefficients.
Mayer's (1750) solution - correct answers-form linear combination of equations
To reduce number of equations to number of unknown coefficients.
These estimates are... (1) but... (1) - correct answers-unbiased estimates of the population parameters
There are an infinite number of linear combinations which are consistent with this procedure. (1)
When you have more than 4 equations, what do you use - correct answers-the method of least squares
Method of least squares - correct answers-process of fitting a mathematical function to a set of
measured points by minimizing the sum of the squares of the distances from the points to the curve
- calculating the vertical distance to the line and square them
- the best model will have the smallest value of d
An estimator is a rule for calculating an estimate of an unknown value using observable data. Mayer's
method gives us a possible estimator but (1) - correct answers-this is not unique
10. An alternative method is to choose estimates of the parameters which minimises the residual sum of
squares:
Least-squares estimator is sometimes known as - correct answers-the ordinary least squares (ols)
estimator
Least-squares estimator improves on mayer's how? - correct answers-it improves on mayer's method
because the variance of the parameter estimates is the lowest possible.
QUESTIONS WITH CORRECT ANSWERS 2025
Regression model is concerned with... (2) - correct answers-modelling the relationship between two or
More variables.
We make regression models to see whether models variables have anything to do with each other
2. Bivariate linear regression model can be written as (1)
Explain each variable (5)
Examples (3) - correct answers-x is the independent or explanatory variable
Y is the dependent or explained variable
U is a random error or disturbance
Α and β are parameters which characterise the relationship between
Y and x. The parameters are not observable directly.
Α - intercept
Β - slope
Examples: income and spending(?), wage and gender,(?) Student high
and exam scores(?)
Two interpretations of the regression mode - correct answers-1. The x values are chosen by the
investigator e.g. By a process of experimentation.
(in this case the x variable is not random and can be treated as being 'fixed in repeated samples')
2. The x and y variables are jointly distributed random variables with cov(x,y) ≠ 0
(this is more realistic for economic data but harder to deal with when deriving the distribution of
estimators)
, 5. What do we try to find out from the linear regression model - correct answers-try to estimate pop
parameters
Y and x are available
What is the problem with the system, (linear regression model)
And what is the solution - correct answers-problem is that system is over-determined - we have more
equations than unknown variables.
Mayer's (1750) solution. Form linear combination of equations to reduce number of equations to
number of unknown coefficients.
Mayer's (1750) solution - correct answers-form linear combination of equations
To reduce number of equations to number of unknown coefficients.
These estimates are... (1) but... (1) - correct answers-unbiased estimates of the population parameters
There are an infinite number of linear combinations which are consistent with this procedure. (1)
When you have more than 4 equations, what do you use - correct answers-the method of least squares
Method of least squares - correct answers-process of fitting a mathematical function to a set of
measured points by minimizing the sum of the squares of the distances from the points to the curve
- calculating the vertical distance to the line and square them
- the best model will have the smallest value of d
An estimator is a rule for calculating an estimate of an unknown value using observable data. Mayer's
method gives us a possible estimator but (1) - correct answers-this is not unique
10. An alternative method is to choose estimates of the parameters which minimises the residual sum of
squares:
Least-squares estimator is sometimes known as - correct answers-the ordinary least squares (ols)
estimator
Least-squares estimator improves on mayer's how? - correct answers-it improves on mayer's method
because the variance of the parameter estimates is the lowest possible.
