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Question 1

How to determine whether a regression line is a good predictor?

Answer 1

r^2 (or R^2) predicts the proportion of variance in Y. It is the coefficient of determination, which is the square of correlation.

Question 2

Prediction interval?

Answer 2

Confidence intervals for predictions of individual Y.

Question 3

!!!Regression towards the mean?

Answer 3

Measure a numerical variable from a set of individuals, and then do it again a second time.

Individuals that are the farthest from the mean on the first measurement will, on average, lie closer to the mean for the second measurement (and vice versa).

Question 4

What to do if Non-linear regression? 3•

Answer 4

•Transformations
•Quadratic regression
•Splines

Question 5

Transformations?

Answer 5

If Y = aX^b, then lnY = lna + b lnX. This is a linear relationship.

If Y = ab^x, then lnY = lna + X lnb

If Y = a + (b/x), then set X’ = 1/x, and calculate Y = a + bX’

All of the equations on the right are linear.

Question 6

Polynomial regression?

Answer 6

Although keeping the intervals in the x axis the same, you change the equation of the x axis parametric that follows a polynomial relationship, like a quadratic.

Question 7

!To avoid over fitting a polynomial regression, the sample size shouldn’t go over?

Answer 7

7 terms

Question 8

The most common way to view non-linear regression closer to a linear regression?

Answer 8

By changing the function of the y axis, like logarithmic scale, called logarithmic transformations.