Question

(1 point) Suppose the relation between CEO’s annual salary in thousands of dollars, salary, and the return on equity, roe, measured as a percentage, is estimated to be: . Now, suppose that salary is measured in hundreds of dollars, rather than in thousands of dollars, say, salarhun. What will be the OLS intercept and slope estimates in the regression of salarhun on roe?

		The new estimates will be equal to the original estimates divided by 10.
		The new estimates will be equal to the original estimates multiplied by 10.
		The new estimates will be equal to the original estimates divided by 100.
		The new estimates will be equal to the original estimates multiplied by 100.
		The new intercept estimate will be equal to the original intercept estimate, and the new slope estimate will be equal to the original slope estimate multiplied by 10.
		The new intercept estimate will be equal to the original estimate of the intercept, and the new slope estimate will be equal to the original estimate of slope divided by 10.
		The new intercept estimate will be equal to the original intercept estimate, and the new slope estimate will be equal to the original slope estimate multiplied by 100.
		The new intercept estimate will be equal to the original intercept estimate, and the new slope estimate will be equal to the original slope estimate divided by 100.
		Nothing. The estimates will stay the same.

Answer 1

We know that:

The regression model is given by:

Also,

Now in our case, salary was measured in thousand of dollars whereas now it is measured in hundreds of dollars,

so, xi' = xi /10 and let be the new slope estimate and be the new intercept estimate.

If we substitute this new xi in the formulae:

Substituting the value of xi' , we get:

      

    

    

  

So, the new slope estimate will be equal to the original slope estimate multiplied by 10.

Similarly,

    

    

So, the new intercept estimate will be equal to the original intercept estimate.