Agresti chapter 12

Question 1

Regression analysis

Answer 1

Y is the response variable and x the explanatory variable

Question 2

Regression model, Population regression equation:

Uy = alpha + Betax.

Answer 2

alpha is a population y-intercept
beta is a population slope.
(parameters, in practice values are unknown)
Uy denotes the population mean of y for all the subjects at a value of x.
* not linear, approximates the relationship: a model

Question 3

Conditional distribution

Answer 3

Probability distribution of y values at a fixed value of x. With an additional parameter of omega describing the SD for each distribution

Question 4

Regression towards the mean

Answer 4

If an x value is a certain number of standard deviations from its mean, then the predicted y is r times that many standard deviations from its mean

Question 5

Total sum of squares

Answer 5

The error measured with the Y-bar (mean, ignoring x):
Sum of (y - y-bar)^2.

Question 6

Proportional reduction in error (asses with squared correlation)

Answer 6

R^2 = sum of squares x residual sum of squares / sum of squares. Between 0 and 1. If r2=0,40, the error using y-hat to predict y is 40% smaller than the error using y-bar to predict y.

Question 7

Property R^2

Answer 7

The closer r^2 is to 1, the stronger the linear association. The more effective regression equation is compared to y-bar to predict y.

Question 8

Ecological fallacy

Answer 8

Making predictions about individuals based on the summary results of groups (should be avoided).

Question 9

Statistical inference about regression

Answer 9

Data gathered using randomization

Population values of y at each value of x follow a normal distribution, with the same standard deviation.