Stat 112: Lecture 10 Notes. Fitting Curvilinear Relationships Polynomial Regression (Ch. 5.2.1) Transformations (Ch. 5.2.2-5.2.4) Schedule: Homework 3 due on Thursday. Quiz 2 next. Curvilinear Relationship.
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This does not affect the that is obtained from the multiple regression model.
Y=Life Expectancy in 1999
X=Per Capita GDP (in US
Dollars) in 1999
Data in gdplife.JMP
Linearity assumption of simple
linear regression is clearly violated.
The increase in mean life
expectancy for each additional dollar
of GDP is less for large GDPs than
Small GDPs. Decreasing returns to
increases in GDP.
The mean of Life Expectancy | Log Per Capita appears to be approximately
a straight line.
By looking at the root mean square error on the original y-scale, we see that
all of the transformations improve upon the untransformed model and that the
transformation to log x is by far the best.
The transformation to Log X appears to have mostly removed a trend in the mean
of the residuals. This means that . There is still a
problem of nonconstant variance.
Fourth order polynomial is the best polynomial regression model
using the criterion on slide 10
Fourth order polynomial is the best model – it has the highest