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Unformatted text preview: maining of the responses from the line. This amount of variation that is not accounted for by the linear relationship is called the SSE. The amount of variation that is accounted for by the linear relationship is called the sum of squares due to the model (or regression), denoted by SSM (or sometimes as SSR). So we have: SSTO = _____ SSM + SSE _________ It can be shown that SSTO SSE SSM r = SSTO
2 = the proportion of total variability in the responses that can be explained by the linear relationship with the explanatory variable x . Note: As we will see, the value of r 2 and these sums of squares are summarized in an ANOVA table that is standard output from computer packages when doing regression. 189 Measuring Strength and Direction for Exam 2 vs Final From our first calculation table (page 186) we have: y y 2 SSTO = ____ = 1300___ From our residual calculation table (page 187) we have: SSE = _____272.1_________ So the squared correlation coefficient for our exam scores regression is: 1300 272 .1 1027 .9 0.791 SSTO SSE
= r2 1300
SSTO Interpretation: We have that 79.1 % of the variation in final exam scores can be accounted for by its linear relationship with exam 2 scores The correlation coefficient is r = . r 2 0.791 0.889 Be sure you read Sections 3.4 and 3.5 (pages 89 – 95) for good examples and discussion on the following topics: Nonlinear relationships Detecting Outliers and their influence on regression results. Affect means, standard deviations so will affect b0 and b1.
Dangers of Extrapolation (predicting outside the range of your data) Dangers of combining groups inappropriately (Simpson’s Paradox) y=
level circles = grade levels
Grade/Age = confounding
variable x = # TV hours Correlation does not prove causation 190 SPSS Regression Analysis for Exam 2 vs Final Let’s look at the SPSS output for our exam data. We will see that much of the computations are done for us. b
Variables Entered/Removed Model
(out of 75) Variables
. Enter a. All reques...
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