week 2 part 6

Question 1

What is A Log-Log Model?

Answer 1

A model where both the dependent and the explanatory variables are transformed into natural logarithms. The model is also called a power regression model

Question 2

What does the log-log model implie depending on the values of β?

Answer 2

• For 0<β1<1 the log-log implies a positive relationship between x and E(y), when x increases, E(y) increases at a slower rate.
• For β1<0 , it suggests a negative relationship: when x increases, E(y) decreases at a slower rate.
• For β1>1, E(y) increases faster than x, resulting in an even faster increase in y relative to x, etc.

Question 3

Where is the log-log model linear?

Answer 3

Not in the variables but in the coefficients. The only condition is that we must first transform both variables to natural logarithms before performing the regression.

Question 4

What does the log-log regression model measure?

Answer 4

The approximate percentage change in y for a small percentage change in x. Thus, β1 is a measure of elasticity.

Question 5

What is a semi-log model?

Answer 5

Where only one of the variables is log-transformed.

Question 6

Which are the two types of semi-log methods?

Answer 6

• The model that transforms the explanatory variable is called a logarithmic model.
• The model that transforms the dependent variable is called an exponential model.

Question 6

When is the logarithmic model particularly useful?

Answer 6

When the explanatory variable is better captured in percentage terms.

Question 7

What does the logarithmic model measure?

Answer 7

The approximate unit change in E(y) when x increases by 1%.

Question 8

What does The Exponential Model measure?

Answer 8

The percentage change in E(y) when x increases by one unit

Question 9

What do we have to do to compare the linear and log-transformed models?

Answer 9

Use an alternative way to calculate R2. R2 = (ryŷ)^2 where ryŷ is the sample correlation coefficient between y and ŷ.