Chapter 11: Regression Analysis I (11.1- 11.3) Simple Linear Regression A positive slope means E(y) increases by the amount B1 for each unit increase in x Intercept is the estimated avg value of Y when x=0; slope measures the estimated change in the avg. value of Y as a result of a 1 unit change Multicollinearity: A condition occurring when two or more independent variables in the same regression model can predict each other better than the dependent variable. Standard error of estimate: variability of the observed y values from the predicted values A high R^2 means a strong relationship between the independent and dependent variables In least-squares regression, best fitting line minimizes the sum of squares of the observed errors A confidence interval for the independent variable x would specify the uncertainty about the mean value of the dependent variable R^2 is the sample correlation coefficient; ex: .2645, 26.45% of the variation in y can be explained by x Correlation: How strong the relationship is. Coefficient correlation: r, ranges from -1 to 1, sign is the same as slope, measures degree of association, no indication of cause and effect relationship Confidence intervals: C.I estimate of expected value of y, will be narrower then prediction interval for x.
Chapter 12: Multiple Regression A) Test parameter significance: shows if there is a linear relationship between all x variables together and y Overall all: H0: B1=B2-B3=0 (no linear relationship); Ha: at least one coeff is not 0 Individual: H0: Bi=0; Ha: Bi =/ 0 or (<,>); test stat= t B)examine variation measures: proportion of variation in y explained by all x variables taken together