Functional Form/Goodness Of Fit

Question 1

If log(y)= Bo +B1X1 + u
What is the interpretation of B1?

Answer 1

B1= the % inc/dec in y if X1 increased by 1 unit

Question 2

If log(y) = Bo + B1X1+u
How would we calculate the % change in y?

Answer 2

% change in y = 100 X B1 X change in X1

Question 3

If y = Bo + B1log(X1) + u
How do we calculate the change in y?

Answer 3

Change in y = (B1/100) X change in X1

Question 4

If log(y) = Bo + B1log(X1) + u
What is the interpretation of B1?

Answer 4

B1= % change in y if X1 increases by 1%
- also known as the elasticity of y w.r.t to X1
- elasticities only used when log-log form

Question 5

If log(y)=Bo+B1log(X1)+u
How do we calculate the % change in y?

Answer 5

% change in y=B1 X % change in X1

Question 6

What is the benefit of using the log functional form?

Answer 6

• can shrink the distribution of variable
• shrinking distribution of y shrinks the distribution of errors
• takes distributions closer to normal
• Allows more reliable use of t- and F-tests
• Useful if relationship between dependent variable and explanatory variable(s) is not linear
• If in log-log form can make use of elasticities which can be useful

Question 7

What is the turnaround point (occurs when using quadratics sometimes)?

Answer 7

When the derivative of y w.r.t of explanatory variable of interest =0

Question 8

When would Rbar-Squared fall?

Answer 8

When an explanatory variable with a t-statistic < 1 is added to the regression

Question 9

When would Rbar-squared increase?

Answer 9

When an explanatory variable with t-statistic > 1 is added to the regression