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Lecture 4

SOC350H5 Lecture 4: Lecture 4

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David Pettinicchio

Lecture 4 Bivariate Regression  Start getting at basic property of regression  Basis of doing model for project  Multivariate regression Regression and Levels of Measurement  Regression that was two variable  Dep and indep  CANNOT DO REG UNLESS DEP VARIABLE IS INTERVAL RATIO  Regression – line on graph that shows slop (relationship)  OLS has to have INTERVAL ratio!  Independent variable can be categorical  Gender is not interval ratio  Comparing effects of females against males and predicting outcome = ok  Dummy variables – dichotomous  How to do regression when outcome is binary  Outcome – if dep variable is interval then use regression  Otherwise use logistic analysis Scatterplot  Graph that is associated with reg is scatterplot  Data points on graph  Quick first step  Look at all points on data and see how dispersed they are  Every point in data represents x and y coordinates  The line is supposed to capture general pattern in data  Relationship between paying higher price to save env and country’s wealth  16 cases  Slide 7 slope interpretation:  “Every one unit increase in x (inequality), y increases by .3”  Ordinary least sq – related to line of fit  Y=mx+b  B is slope  A is intercept Best fitting line  Every line can be equated to y=a+bx  Spss giving best fitting line  When it fits line to data  You fit line to reduce total amount of error squared  Sq to accommodate for negative (points under line)  Line of fit is line that reduces total number of error – related to ordinary least sq  Good predictions make least amount of error  When you make predictions using your graph – want to reduce total amount of error sq  Best fitting line has the hat  It could otherwise be any line Errors  OLS has least amount of errors associated with it – residual (left over that is not explained)  Using line of fit formula to predict  Predict for x=20  Actually in graph, x=20 when y=40  But you get y=41.8 with line equation  Y-y = predicting with an error of 1.8 Residual sum of squares  If line of fit has least amount of error – minimizing sum of all error squared  Crappy model = crappy error = crappy prediction  SPS
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