B16 Regression Models for Nonlinear Relationships

Question 1

When is the quadratic regression model appropriate

Answer 1

In U shaped relationships where it changes from negative to then become strongly positive or the opposite. y = b0 + b1x + b2²x

Question 2

Are the coefficients easily interpreted in a quadratic regression model

Answer 2

The book does not think so but I guess it is a matter of perspective, It does not hurt to plot it though.

Question 3

What is the aproximate marginal effect on y in a quadratic regression model

Answer 3

b1 + 2*b2x aka the deriviative of the function, when this is zero the maximum or minimum point when this is zero

Question 4

What is a polynomial regression model

Answer 4

A regression model with an explanatory function that is a polynome, aka it is made up of various degrees of exponentiations of x. A linear regression model is a polynomial regression model of order one while a quadratic regression model is a polynomial regression model of order 2.

Question 5

What order of polynomial regression model is a cubic regression model

Answer 5

order 3

Question 6

What is the function for the regression log-log model

Answer 6

ln(y) = b0 + b1*ln(x) + residual

Question 7

If y is e^x what is ln(y)

Answer 7

x

Question 8

what is e^ln(x)

Answer 8

x

Question 9

In the log-log model if B1 is between 0 and 1 is the relationship positive or negative

Answer 9

Positive but marginally decreasing

Question 10

What if B1 is less then zero in the log-log regression model

Answer 10

A sharp negative relationship around zero that mellows out untill it approaches a constant relationship

Question 11

Can you convert the log-log regression model to a linear regression model

Answer 11

Yes if you ignore that x and y are logs. This will make the function be one of percentage change in y for x each aditional percentage change in x.

ln(y) = b0 + b1ln(x) + u => y% = b0 + b1x% + u

Question 12

B1 is a mesure of elasticity in the log-log regression model

Answer 12

True

Question 13

Why should you use unrounded coefficients or at least 4 decimals in the log-log regression model

Answer 13

Becouse small changes make a big diference in the world of logarithmics

Question 14

What is a semi log regression model

Answer 14

One where some but not all variables are transformed to logarithms when describing their relationship.

Question 15

What is a semi log model called that only transforms the explanatory variable x called

Answer 15

A logarithmic model

Question 16

What is a semi-log model called that only transforms the response variable y called

Answer 16

A exponential model

Question 17

log-log and logarithmic models can create similar shapes

Answer 17

True

Question 18

Explain in words what the logarithmic regression model shows

Answer 18

The expected change in y when x changes by 1%

Question 19

Explain in words what the exponential regression model shows

Answer 19

The expected percentage change in y when x changes by one unit

Question 20

Can you compare models that use different response variables

Answer 20

No so one model that returns y is not nececarily better than one that returns ln(y) if R² is higher