Chapter 13 Simple Linear Regression

unexplained variation

(error sum of squares) represents variation due to factors other than the relationship between X and Y

residual

(estimated error value) is the difference between the observed and predicted values of the dependent variable for a given value of X

independent variable

(explanatory variable) the variables used to make predictions. X

equal variance assumption of regression

(homoscedasticity) requires the variance of the errors be constant for all values of X

explained variation

(regression sum of squares) represents variation that is explained by the relationship between X and Y

dependent variable

(response variable)the variable you wish to predict. Y

total sum of squares

(total variation) measure of the variation of the Yi values around their mean, Y-bar

Y intercept

mean value of Y when X equals 0

coefficient of determination

measures the proportion of variation in Y that is explained by the variation in the independent variable X in the regression model

standard error of the estimate

measures the variability of the observed Y values from the predicted Y values

residual analysis

visually evaluates the regression assumptions to determine whether the regression model is appropriate

Assumption of Regression

Linearity, independence of errors, normality of error, and equal variance

least-squares method

determines the values of the regression coefficients that minimize the sum of squared differences around the prediction line

regression analysis

enables you to develop a model to predict the values of a numerical variable based on the value of other variables

slope

expected change in Y per unit of X

relevant range

includes all values from the smallest to the largest X used in developing the regression model. You should not extrapolate beyond the range of X values

independence of errors assumption of regression

particularly important when data are collected over time--the errors of a specific time period are sometimes correlated with those of a previous time period

autocorrelation

pattern when data are collected over sequential time periods because a residual at any one time period is sometimes similar to residuals at adjacent time periods.

SLR prediction line

predicted value of Y equals the Y intercept plus the slope multiplied by the value of X

normality assumption of regression

requires that the errors be normally distributed at each value of X

regression coefficients

sample Y intercept and sample slope

simple linear regression

single numerical independent variable, X, is used to predict numerical dependent variable Y

Durbin-Watson statistic

used to measure autocorrelation