Suppose that we estimate sales by a firm as a function of the average education

Question

Suppose that we estimate sales by a firm as a function of the average education level of employees. log(sales) = beta_0 + beta_1 education + u sales is measured in dollars per years, and education is measured in average years of post-secondary education across employees within the firm. a. Suppose you estimate beta_1 = 0.07. If assumptions 1-4 hold, interpret beta_1 from the log-level regression above. b. Suppose again that beta_1 = 0.07 and the covariance between education and log(sales) is 2. What is the variance of education within the sample?

Explanation / Answer

Solution

Part (a)

In the linear regression equation, Y = 0 + 1X + , 1 represents the slope the regression line and in physical terms, it represents the average change in Y per unit change in X, positive 1 implies Y decreases/increases by 1 units when X decreases/increases by one unit and negative 1 implies Y decreases/increases by 1 units when X increases/ decreases by one unit.

Going by the above interpretation, 1 = 0.07 =>average log(sales) will increase/decrease by 0.07 units when number of post-secondary education increases/decreases by 1 year.

Part (b)   

Least square estimate of 1 = cov(X,Y)/Var(X). So, we have , 0.07 = 2/Var(X) or Var(X) = 2/0.07 = 28.57 ANSWER

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