week 2 part 5 Flashcards
Why can we capture non-linear relationships within the framework of a linear regression model by making simple transformations of the response and/or explanatory variables?
Because the assumption of linearity imposes a restriction of linearity on the parameters, not on the variables.
What does the quadratic regression model capture?
Cases where the effect of x on y changes in size and direction.
How do we determine whether the quadratic or linear model is better suited?
We look at the adjusted R2.
What is different with the quadratic regression model?
The effect of x on y is not constant but varies depending on the value of x. Therefore it is better to calculate and visualize the expected effect on the response variable over a range of values for the explanatory variable.
What does the marginal effect depend on in the quadratic regression model?
The value of x being evaluated.
When does y(hat) reach a maximum or minimum?
When the marginal effect is zero you reach:
Maximum: if b_2<0
Minimum: if b_2 > 0
How do you find the value of x when y(hat) is maximized or minimized?
b1+2b2x=0 vilket ger
x= -b1/(2*b2 )
What is the polynomial regression model of order 3 called?
The cubic regression model.
How do we describe polynomial regression models?
Polynomial regression models describe various numbers of sign changes.
* No sign change: Polynomial regression model of order 1.
* One sign change: Polynomial regression model of order 2.
* Two sign changes: Order 3, and so on!
What is Another way to capture non-linear relationships between the response variable and the explanatory variable?
Using the natural logarithm, which is the inverse of the exponential function.
What is the exponential function?
y=exp(x)=e^x where e≈2.718 is a constant and x is the argument of the function.
What is the natural logarithm?
Ln(y)=x where ln(y) is the natural log of y.
Which values can we log-transform?
Only variables with positive values!
What do we have to think about when we use logarithms?
The natural logarithm converts changes in a variable into percentage changes.
