Week 5: Assumptions Part II: Specification Error

Question 1

Linearity

Answer 1

The effect of X on Y is the same regardless of the level of X

Question 2

Nonlinearity

Answer 2

The effect of X on Y is different for different levels of x

Question 3

Kinds of nonlinearity

name 7

Answer 3

• Increaslingly positive: The effect of X on Y is positive and becomes stronger (more positive) as X increases
  (b1 > 0, b2 > 0)
• Diminishing positive: The effect of X on Y is positive and becomes less strong (less positive) as X increases
  (b1 > 0, b2 < 0)
• Increasingly negative: The effect of X on Y is negative and becomes stronger (more negative) as X increases
  (b1 < 0, b2 < 0)
• Diminishing negative: The effect of X on Y is negative and becomes less strong (less negative) as X increases
  (b1 < 0, b2 > 0)
• The effect of X on Y is positive until a point (and becomes less strong as X increase) after which it is negative (and becomes more strong as X increases) Parabol (b1 = 0, b2 < 0)
• Logistic growth: Y stays very close to 0 as X increases then rapidly approaches a turning point after which it rapidly approaches and stays very close to 1

Poisson distribution: A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.

Question 4

Additivity

Answer 4

The effect of X1 on Y is the same regardless of the level of X2

Question 5

Nonadditivity

Answer 5

The effect of X1 on Y is different for different levels of X2

a non-additive relationship is called an interaction between two or more variables