1. 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

2. Correlation

3. Correlation Matrix

4. Analytics & History: 1st Regression Line
The first “Regression Line”

5. 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

6. Which line fits the best?

7. Sum of Squares Total sum of squares Model sum of squares
Residual sum of squares F R2

8. 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

10. 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

11. 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)

12. Correlation

13. Model 1

15. Testing the Model: R2 R2
The proportion of variance accounted for by the regression model.
The Pearson Correlation Coefficient Squared
Slide 15

16. Residuals

17. Prediction
predict(model.1)
heights$model1 <- predict(model.1)

19. 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

20. Box Plot

21. Descriptive Stats: Box Plot

22. Regression: Children Heights~Gender
model.5 <- lm(childHeight~gender, data = h)

23. 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

24. Model Specification & Prediction
Outcome = (Model) Error
Height = *father mother Gender + error
Gender:
Male:
Female: 0