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Published byMelvyn Young Modified over 9 years ago
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Continuous Outcome, Dependent Variable (Y-Axis) Child’s Height
Histogram Continuous Scatter Predictor Variable (X-Axis) Parents Height Categorical Boxplot Gender Regression Model Linear Regression
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Correlation
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Correlation Matrix
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Analytics & History: 1st Regression Line
The first “Regression Line”
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Describing a Straight Line
Regression coefficient for the predictor Gradient (slope) of the regression line Direction/strength of relationship b0 Intercept (value of Y when X = 0) Point at which the regression line crosses the Y- axis (ordinate) Slide 5
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Which line fits the best?
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Sum of Squares Total sum of squares Model sum of squares
Residual sum of squares F R2
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Sum of Squares SST SSR SSM
Total variability (variability between scores and the mean). SSR Residual/error variability (variability between the regression model and the actual data). SSM Model variability (difference in variability between the model and the mean). Slide 8
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Testing the Model: ANOVA
SST Total Variance in the Data SSM Improvement Due to the Model SSR Error in Model If the model results in better prediction than using the mean, then we expect SSM to be much greater than SSR
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Linear Model - Regression
lm() function – lm stands for ‘linear model’. Model <-lm(outcome ~ predictor(s), data = dataFrame, na.action = an action)) model.1 <- lm(childHeight~father, data = heights)
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Correlation
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Model 1
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Testing the Model: R2 R2 The proportion of variance accounted for by the regression model. The Pearson Correlation Coefficient Squared Slide 15
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Residuals
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Prediction predict(model.1) heights$model1 <- predict(model.1)
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Compare Models 0.385 Model 1 2 12 3 4 Intercept 40.1 46.6 22.6 22.63
22.64 Father 0.385 0.36 0.01 Mom 0.314 0.29 NA midparentHeight 0.637 0.538 R-squares 0.070 0.0395 0.105 0.102 0.1033 r 0.27 0.2 0.32 R^2 0.073 0.04
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Box Plot
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Descriptive Stats: Box Plot
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Regression: Children Heights~Gender
model.5 <- lm(childHeight~gender, data = h)
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Linear Regression Comparison
Model 1 2 12 3 4 5 6 7 Intercept 40.1 46.6 22.6 64.1 16.5 Father 0.385 0.36 x 0.39 Mom 0.314 0.29 0.31 midparentHeight 0.637 0.538 0.687 Gender 5.13 5.21 R-squares 0.070 0.0395 0.105 0.102 0.1033 0.5137 0.632 0.634 r 0.27 0.2 0.32 0.717 R^2 0.073 0.04
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Model Specification & Prediction
Outcome = (Model) Error Height = *father mother Gender + error Gender: Male: Female: 0
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