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1. Function lm() in R and its Basic Parameters Jiong Xun

2. Learning Objectives Understand linear regression Understand purpose of lm() function Using lm() to fit regression models Interpret output of lm() function

3. Ever Wondered How… Maps are able to estimate your travelling time Surcharge pricing are determined to meet demands for taxi HDB resale prices are forecasted

4. What is Linear Regression? Interested in the relationship between a dependent variable (y) and one or more independent variables (x) Models relationships between variables Simple Linear Regression (1 independent variable) Multiple Linear Regression (2 or more independent variables) Finds best-fit line that minimises distance between observed data values and predicted values

5. How do we obtain best-fit line?

6. Ordinary Least Squares Find the best-fit line ⇒ want the line to be as close to data points as possible Minimise vertical distance between each point to line Residual Sum of Squares (RSS) ⇒ squared sum of residuals for all data points Squared as we do not want residuals to “cancel off” one another Minimise RSS Minimum total distance between line and points Best-fit line

7. Visualised on a Simple Plot Actual Data Points Residuals Regression Line

8. How to We Use R to plot Linear Regression Model?

9. Syntax of lm() Function lm() ⇒ stands for linear model

10. Example Dataset “trees” Inches ft Cubic ft

11. Example Dataset “trees” Y variable (response) X variable (explanatory) Name of data frame that model is using

12. Example Dataset “trees”

13. Example Dataset “trees” Difference between observed and predicted values

14. Example Dataset “trees”

15. Example Dataset “trees” Used to predict value of the response variable

16. Example Dataset “trees”

17. Example Dataset “trees” Average amount that estimate varies from actual value

18. Example Dataset “trees”

19. Example Dataset “trees” t value = Estimate / std. Error

20. Example Dataset “trees”

21. Example Dataset “trees” p-value for the t-test to determine if coefficient is significant

22. Example Dataset “trees”

23. Example Dataset “trees” Standard deviation of the residuals Number of data points that went into estimation

24. Example Dataset “trees”

25. Example Dataset “trees” Gives a measurement of what % of variance in response can be explained by the regression

26. Example Dataset “trees”

27. Example Dataset “trees” Indicates if model as a whole is statistically significant

28. Example Dataset “trees” Predict Volume of tree based on Girth and Height of tree?

29. Example Dataset “trees”