Consider the following multiple regression models of R&D expenditures based upon data from 32 firms in the chemical industry:

rd_i = β₁ + β₂ sales_i +β₃salessq_i + β₄profits_i + e_i (1)

lrd_i = β₁ + β₂ lsales_i + ei (2)

where,

r_d = R&D spending by firm (millions of $)
sales = firm sales (millions of $)
salessq = square of sales (sales2)
profits = firm profits (millions of dollars)
lrd = log(rd)
lsales = log(sales)

The file rdchem.dta contains data on R&D expenditures, sales, and profits for 32 firms. This assignment includes the estimation of a multiple regression model and hypothesis tests of the regression parameters.

1. Stata assignment

Using all the observations in the data file,

a. Obtain descriptive statistics for all the variables used in the regression models given by eqn (1) and eqn (2).

b. Estimate the regression model given by equation (1) above

c. Using Stata, test the null hypothesis, H0: β2 = β3 = 0 in equation (1)

d. Estimate the regression model given by equation (2) above

e. Submit the original log file (in .smcl format) containing the results of a-d above.

Note:

Your name must be part of the name of the log file you open at the beginning of the Stata session, e.g., richard-smith_assignment3.smcl

2. Written assignment

Answer the following questions on the basis of the Stata output (additional calculations are not necessary):

a. Report the estimated regression (in equation format) for equation (1) obtained above by applying the Stata software (Do not copy and paste the regression output table from Stata). Is each estimated coefficient statistically significant (at the .05 level)? Test the hypothesis for overall significance of the model.

b. Using a level of significance = .05, interpret the results of the hypothesis test in part c. of the Stata assignment above (using an alternative hypothesis H1: Either β2 or β3 is nonzero). Interpret your decision.

c. Report the estimated regression for equation (2). Interpret the coefficient of lsales in equation (2). Is it statistically significant? What information does this coefficient provide about the relationship between R&D expenditures and sales?

d. Write a paragraph about the main findings from this assignment about R&D expenditures and its determinants. (You may use Stata to obtain critical values for the test statistics or use the tables at the end of the book)

3. Submit Assignment 3 via Blackboard with the following two attachments: Stata .smcl log and Word file