Suppose that we estimate the following simple linear regression model by the met

Question

Suppose that we estimate the following simple linear regression model by the method of Least Squares: y_i = beta_0 + beta_1 x_i + epsilon_i; epsilon_i ~ N[0, sigma^2]; i 1, 2, 3, ..., n (i) If the y variable has units of $'000, and the x variable has units of $, what are the units of the Least Squares estimators, b_0 and b_1? (ii) Suppose that the units of measurement for the x variable are changed to hundreds of $'s. What will happen to the values of b_0 and b_1. (iii) With this change of units, what will happen to the predicted values of the v variable?

Explanation / Answer

Answer i

The units of b0 will be $'000 and the units of b1 will be $'000/$ or $'000.

Answer ii

When the units of x variable are changed, there will be no change in the units of b0, the units of b1 will be $'000/$'000, that is, units of b1 will be in $.

Answer iii

There will be no change in the units of the predicted values of y variable.

Thanks.

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