1. A little VOCAB

2. Causation
Causation is the "causal relationship between conduct and result". That is to say that causation provides a means of connecting conduct with a resulting effect, typically an injury
Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events. This is also referred to as cause and effect.

3. Confounding
In statistics, a confounding variable (also confounding factor, a confound, or confounder) is an extraneous variable in a statistical model that correlates (directly or inversely) with both the dependent variable and the independent variable.

4. Transforming Data to perform Linear Regression
Non-linear Data
Transforming Data to perform Linear Regression

5. What to do if the data is not linear…
Calculate the LSRL
Transform data:
Is the residual plot scattered? NO
YES
Appropriate model

6. Let’s examine this data set.
This shows the monthly premium for Jackson National’s 10-year Term Life Insurance Policy of $100,000 for males and females (smoker & non-smoker) at a given age.

7. Looking at just the premium for males, we see that the data is not linear

8. Cool – it’s a piece-wise function!
Separate LSRLs are fitted to different age ranges that have been transformed using logs
Cool – it’s a piece-wise function!

9. Example 1: Consider the average length and weight at different ages for Atlantic rockfish.

10. Use your calculator to draw a scatterplot of the data for length (x), in L1 and weight (y), in L2. Is it linear? ____ Is there a pattern? _____ Since there is a pattern, let’s try to “straighten” the data.

11. Since length is __ dimensional and weight (which depends on volume) is __ dimensional, let’s graph length3 (x), in L3 vs. weight (y) in L2. Is the scatterplot linear? ____
Highlight L3 ENTER
L1 ^ 3 ENTER

12. Calculate the LSL on the transformed points (length3, weight) and determine r2.

13. Predict the weight of an Atlantic Rockfish that is 31.5cm long.

14. The residual clearly has a pattern, so we must transform it!

16. COmpuTER OUTPUT

17. Be sure to convert r2 to decimal before taking the square root!
Computer-generated regression analysis of knee surgery data:
Predictor Coef Stdev T P
Constant
Age
s = R-sq = 30.6% R-sq(adj) = 23.7%
Be sure to convert r2 to decimal before taking the square root!
NEVER use adjusted r2!
What is the equation of the LSRL?
Find the slope & y-intercept.
What are the correlation coefficient and the coefficient of determination?