Review of Regression Basics
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1 Review of Regression Basics When describing a Bivariate Relationship: Make a plot Strength, Direction, Form Model: yhata+b Interpret slope in contet Make Predictions Residual ObservedPredicted Assess the Model Interpret r Residual Registrations (thous) Registrations (thous) Registrations (thous) Killed (. thous^)registrations Killed (. thous^)registrations.; r.; r.. Registrations (thous) Killed (. thous^)registrations Killed (. thous^)registrations ; r ; r..
2 Reading Minitab Output Regression Analysis: Fat gain versus NEA The regression equation is FatGain ****** + ******(NEA) Predictor Coef SE Coef T P Constant.... NEA.... S. RSq.% R Sq(adj).% Regression equations aren t always as easy to spot as they are on your TI. Can you find the slope intercept above?
3 Outliers/Influential Points Age Age at at First First Word Word Gesell Gesell Child Child Age Age Does the age of a child s first word predict his/her mental ability? Consider the following data on (age of first word, Gesell Adaptive ) for children. Age Age at at First First Word Word Gesell Gesell Age Age () () (. (. (. (. ^)Age ^)Age + + ; + ; ; ; r r r.... Influential? Does the highlighted point markedly affect the equation of the LSRL? If so, it is influential. Test by removing the point finding the new LSRL.
4 Hubble Hubble data data Eplanatory vs. Response The Distinction Between Eplanatory Response variables is essential in regression. Switching the distinction results in a different leastsquares regression line r r v v r r ; ; r r.. Hubble Hubble data data v v r r.v.v + +.;.; r r.. Note: The correlation value, r, does NOT depend on the distinction between Eplanatory Response.
5 Beer Beer Blood Blood Alcohol Alcohol Beers Beers BAC BAC.Beers.Beers.;.; r r.. Correlation There is a weak, positive, linear relationship between y. However, there is a strong nonlinear relationship. r measures the strength of linearity... The correlation, r, describes the strength of the straightline relationship between y. E: There is a strong, positive, LINEAR relationship between # of beers BAC. Collection Collection y y ; ; r r..
6 Coefficient of Determination The coefficient of determination, r, describes the percent of variability in y that is eplained by the linear regression on. Wine Wine Consumption Heart Heart Disease Disease Alcohol Alcohol (L/yr) (L/yr) DeathRate DeathRate (. (. yr/l)alcohol yr/l)alcohol + ; ; rr.. % of the variability in death rates due to heart disease can be eplained by the LSRL on alcohol consumption. That is, alcohol consumption provides us with a fairly good prediction of death rate due to heart disease, but other factors contribute to this rate, so our prediction will be off somewhat.
7 Cautions Correlation Regression are NOT RESISTANT to outliers Influential Points! Correlations based on averaged data tend to be higher than correlations based on all raw data. Etrapolating beyond the observed data can result in predictions that are unreliable.
8 Correlation vs. Causation Consider the following historical data: Collection Collection Year Year Ministers Ministers Rum Rum Collection Collection y y + + ; ; r r.. There is an almost perfect linear relationship between y. (r.) # Methodist Ministers in New Engl y # of Barrels of Rum Imported to Boston CORRELATION DOES NOT IMPLY CAUSATION!
9 Summary Registrations (thous) Killed (. thous^)registrations Killed (. thous^)registrations.; r.; r.. Killed (. thous^)registrations Killed (. thous^)registrations ; r ; r..
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