Question

1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is the relationship between Bo and Bo, and the relationship between 2 and 3? e) What does it mean for 2o and B, to be unbiased? Under which assumptions are so and B unbiased? 1) Graph an example model with data points showing that EwX: 0, but Varu, X:] =? 8) Graph an example model with data points showing that EMIX) = 0, but Varu|X10?

f and g

Answer 1

2 - 2, + %; + М.: - - 13, + 13, X: +4; ---

f and g Solution: the question means error term doesn't have zero mean but error variance is constant. the normal curves around the Xi values represents the distribution of the error term. in the question f error term has constant variance hence the constant spread of the normal distribution but mean is not centred around the regression line hence error mean is not zero. but in the case g the error terms doesn't have constant variance(hence the unequal spread) but their mean is zero.