Question

the following equation was obtained by OLS:

log(salary) = 4.32 + 0.310log(sales) + 0.0191roe + 0.00025ros

(0.26) (0.031) (0.0049) (0.00056)

You can see the corresponding (heteroskedasticity-robust/White) standard errors in parentheses below the coefficients. In addition, you know from the output that n = 210 and R2 = 0.291. By what percentage is salary predicted to increase if ros increases by 50 percentage points? (Answer with a whole interpretation sentence!) Does ros have a practically large effect on salary? (To phrase the question differently: Is the effect economically significant?)

Answer 1

Interpretation of the slope coefficient of variable ros

When ros increases by 1 percentage point, then on an average salary increases by 0.00025 percentage point, keeping other variables constant.

So, when ros increases by 50 percentage points, then on average, salary is predicted to increase by 0.0125 percentage points., i.e, (50 × 0.00025)., keeping other variables constant.

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To check whether ros have large effect on salary or not

Following hypothesis test is conducted,

H_O : β = 0 {ros have no significant impact on salary}

H_A : β ≠ 0 {ros have significant impact on salary}

Using   = 0.00025 and standard error = 0.00056, calculate t-statistic as follows,

Thus, the calculated t- statistic is equal to 0.446.

Now, at a 5% level of significance and (n-2) = 208 degrees of freedom, the critical t-value is equal to 1.96.

Decision rule

Since, calculated t -statistic equal to 0.446 is less than the critical t-value equal to 1.96. Thus, the null hypothesis is accepted.

This implies that the ros have no significant impact on salary.

Thus, it can be concluded that ros have practically no large effect on salary, i.e, it is economically insignificant.