Suppose you analyze the relationship between wages in dollars (wage) and height
ID: 1252937 • Letter: S
Question
Suppose you analyze the relationship between wages in dollars (wage) and height in inches (height), and obtain the following results: wage = 32519 + 532 height You are invited to present these results at an international conference. At the last minute. however, you realize the attendees will not be familiar with imperial units, so you would like to instead present the results from this regression: wage = beta 0 + beta 1 heightcm + u where height is measured in centimeters (heightcm). Can you derive the OlS estimates of beta 0 and beta 1 from your original regression results? (For simplicity, assume 1 cm = 0.4 inches.)Explanation / Answer
Not much time left for this question, and my econometrics is a bit rusty.
If I remember correctly, since we assume that 1 cm = 0.4 inches, given that your height is in inches, the relationship between the two is 1in = 2.5cm.
Since the effect is now basically multiplied due to the conversion (by 2.5 times), you would have to divide the 1 by 2.5 to maintain the OLS relationships, so the equality holds.
B1*height(inches) = (B1/2.5)*(height inches)*(2.5cm/inch)
So basically, it should look like this: wage = 0 + (B1/2.5) * (heightcm) +
The intercept and error should remain same.
Be aware that if the change is in units on the left hand side of the equation, i.e. the "wage", to maintain equality, both the intercept and coefficient will be divided / multiplied by whatever factor affected the "wage"
Hope it helped.