�

= 2.613 + 0.003 sales – 0.000000007 2

The following equation was obtained by OLS:

(0.429) (0.00014) (0.0000000037) N= 32, 2=0.1484

Rdintens represent company’s R&D.

(1) At what point does the marginal effect of sales on rdintens become negative?

(2) Would you keep the quadratic term in the model? Explain.

(3) Define salesbil as sales measured in billons of dollars: salesbil = sales/1000.

Rewrite the estimated equation with salesbil and 2 as the independent variables. Be sure to report standard errors and R-squared.

There is an equation that was estimated as follows:

� =1028.10 + 19.30 hsize – 2.19 h 2 – 45.09 female – 169.81 black

equation, what is the optimal high school size?

(2) Holding hsize fixed, what is the estimated difference in SAT score between

nonblack females an nonblack males? How statistically significant is this

estimated difference?

(3) What is the estimated difference in SAT score between nonblack females and

nonblack males? How statistically significant id this estimated difference?

Which of the following ar e consequences of heteroskedasticity? (1) The Ols estimators, � are inconsistent.

(2) The usual F statistic no longer has an F sidtribution. (3) The Ols estimators are no longer BLUE.

(6.29) (3.83) (0.53) (4.29) (12.71) +62.31 female *black

(18.15)

N= 4137, 2=0.0858

SAT is the combined SAT score, hsize is the student’s high school graduating class, in hundreds, female is a gender dummy variable, and black is a race dummy variable eauql to one for blacks and zero otherwise.

(1) Is there strong evidence that h 2 should be included in the model? From this