What is the least squares estimate of ß1

Reference no: EM13189135

1. Consider the simple linear regression model without an intercept, y = ß1x + u, with the assumption E(u|x)=0. Also assume that E(x)=0

a. Show that E(y)=0 and using this as well as E(x)=0 show that the covariance between x and y is given by E(xy) and that the variance of x is given by E(x2 )

b. Using the results in a. and the assumptions above show that E(xu)=0 and hence that ß1 = E(xy) / E(x2 )

c. What is the Least Squares estimate of ß1 (say ß~ ) in this model without an 1 intercept? How does it relate to the population value ß1 ? Do they have to be the same - Why? Why not?

Reference no: EM13189135

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