A researcher is regressing log(salary) (logarithm of CEO’s salary) on the explan

Question

A researcher is regressing log(salary) (logarithm of CEO’s salary) on the explanatory variables log(sales) (the logarithm of sales), roe (the return on equity, expressed in percentage form), and ros (the return on the stocks, expressed in percentage). The results of the estimation are:

log(salary) = 3.22 + 0.308 log(sales) + 0.0223 roe + 0.00048 ros. The standard errors are 0.36 for the constant, 0.039 for log(sales), 0.005 for roe, and 0.00059 for ros.

Let 1 and 2 denote the coefficients associated with log(sales) and roe, respectively. Given the provided information, can you construct a 95% confidence interval for 1 + 2? If not, what information would you need?

Thanks!

Explanation / Answer

NO. We can't construct confidence interval of  1 + 2

we need combined variance of of  1, 2 to find the 95% confidence interval

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