Lecture 8 - Interpolation vs Extrapolation, Influential Observations, Confound, Lurking Variable

Question 1

Question

Which of the following CANNOT be done using a simple linear regression equation?

A) Determine whether the association is linear or non-linear
B) Predict the value of 𝑦 for a particular value of 𝑥
C) Estimate the slope between 𝑦 and 𝑥
D) Estimate whether the linear association is positive or negative.

Answer 1

A) Determine whether the association is linear or non-linear

A simple linear regression equation assumes a linear relationship between the independent variable x and the dependent variable y. It cannot be used to determine whether the association is linear or non-linear. If the relationship is non-linear, other models (such as polynomial regression or non-linear regression) should be used instead.

Question 2

Question

Answer 2

Question 3

Interpolation vs Extrapolation

Answer 3

Question 4

Answer 4

Question 5

Compute the Correlation

Answer 5

Question 6

Question

What is the value of the correlation?

A) 0.8076
B) 0.7691
C) 0.8986
D) -0.8986
E) None of the above

Answer 6

Question 9

Answer 9

D) It will decrease by 0.30730

Question 10

Answer 10

A) 2.59 mm/y

Question 11

Answer 11

C) It would not be appropriate to make this prediction

Extrapolation Required

Question 12

Outliers and
Influential Observations

Answer 12

Question 13

Adding an Outlier

Answer 13

Question 14

Notes:

Influential observation

Answer 14

Has a large influence on the statistical calculations being done

Question 15

Notes:

Identification of “Influential Observation”

Under certain scenarios, the investigator may choose to remove such points from the analysis

Answer 15

• If removing it from the data causes our line of best fit to change markedly (see previous example), then its an influential observation.

Investigators should try to determine if it’s due to an error or some other factor surrounding the unit/process from which this observation was collected.

Question 16

Limitations

Lurking Variable

Answer 16

Question 17

Confounding

Example: Weight and age are confounding variables for height in children

Answer 17

Two variables (either explanatory variables or lurking variables) are
confounded when their effects on a response cannot be distinguished
from each other.

weight and age cannot be distinguished from one another when looking at height

Question 18

Activity: Suppose you want to study the effect of diet and exercise on a person’s blood pressure.

What is the response variable? The explanatory variable(s)?

What lurking variable(s)?

Answer 18

Respone: Blood Pressure
Explanatory: Diet/Exercise

Lurking Variables: medication, lifestyle, gender, race, etc.