A little VOCAB

 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. Causation

 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. Confounding

Non-linear Data Transforming Data to perform Linear Regression

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

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.

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

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

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

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.

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

Calculate the LSL on the transformed points (length 3, weight) and determine r 2.

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

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