chapter 10 - linear regression

regression

prediction of one variable from knowledge of one or more other variables, not symmetrical, outliers have large effect (any score >3 SD from mean), in absence of any other info the best prediction is always group mean

simple regression

using only one predictor and one criterion

linear regression

relationship is linear

curvilinear regression

best fit line is a curve

predictor variable (x)

variable from which a prediction is made, ie. ice cream sales

criterion variable (y)

variable to be predicted, ie. murder rate

regression equation

ŷ = bX + a, where ŷ is predicted value of y, b is slope of regression line, and a is y intercept when x=0

plotting a line

pick two different values of x at either extreme, compute ŷ for each, plot the two points and then connect them

error/residual

the difference between ŷ and y, can be measured using the SD from the difference (standard error of the estimate)

standard error of the estimate

the average of the squared deviations about the regression line, interpret as “the SD of points about the regression line is ___”, want this value to be small, the square of the standard error of the estimate is called residual/error variance

measures of predictable variance (r²)

square the correlation, meaning X accounts for __% of the variability in Y

standardized regression coefficient beta (B)

results from data that has been standardized, when you have one predictor variable and standardized data then r=B, in SD units