For the simple regression Yi = + Xi + ui considered in Chapter 3, show that (a) OLS = n i=1 xiyi/ n i=1

For the simple regression Yi = α + βXi + ui considered in Chapter 3, show that

(a) βOLS =

n i=1 xiyi/

n i=1 x2i can be obtained using the residual interpretation by regressing X on a constant first, getting the residuals ν and then regressing Y on ν.

(b) αOLS = ¯ Y − βOLS

¯X can be obtained using the residual interpretation by regressing 1 on X and obtaining the residuals ω and then regressing Y on ω.

(c) Check the var(αOLS) and var(βOLS) in parts

(a) and

(b) with those obtained from the residualing interpretation.