Mathematics 3 Statistics Chapter 2 DESCRIPTIVE STATISTICS PART

Mathematics 3 – Statistics Chapter 2: DESCRIPTIVE STATISTICS – PART II

What Do We Mean with Paired Data? � Chapter 2: DESCRIPTIVE STATISTICS – PART II 2

How Can We Represent Paired Data? � Chapter 2: DESCRIPTIVE STATISTICS – PART II 3

What Do Scatter Diagrams Tell Us? � We can often see some kind of association between the variables: § Positive association: When the larger values of the explanatory variable are associated with larger values of the response variable. § Negative association: When the larger values of the explanatory variable are associated with smaller values of the response variable. � � The relationship might be linear or curved or there might be no underlying form. If there is a relationship it may be strong or weak. Chapter 2: DESCRIPTIVE STATISTICS – PART II 4

Examples of Scatter Diagrams Chapter 2: DESCRIPTIVE STATISTICS – PART II 5

Examples of Scatter Diagrams (continued) � Refer to Example 1. 1: d) Compare the POE and WIM method using scatter plot. e) Do the measurement errors (i. e. differences between WIM and POE measurements) depend on the speed of trucks? Create a scatter diagram which could help you with this question. f) Do you thing that WIM method is a good substitute for POE method? � Example 2. 1, part a) on my personal website. Chapter 2: DESCRIPTIVE STATISTICS – PART II 6

Correlation � Chapter 2: DESCRIPTIVE STATISTICS – PART II 7

� Chapter 2: DESCRIPTIVE STATISTICS – PART II 8

Simulated Data r=1 20 18 18 16 14 14 12 12 10 10 y y 16 8 8 6 6 4 4 2 2 0 0 2 4 6 8 10 X 12 14 16 18 0 20 r = 0. 988 20 0 2 4 6 8 10 X 12 14 16 18 20 r = -0. 569 20 18 18 16 16 14 14 12 12 10 y y 10 8 8 6 6 4 4 2 2 0 r = -1 20 0 2 4 6 8 10 X 12 14 16 18 20 0 0 2 4 2: DESCRIPTIVE 6 8 10 Chapter STATISTICS – PART IIX 12 9

Simulated Data (continued) r≐ 0 20 18 18 16 14 16 12 14 y y 10 8 12 6 4 10 8 2 0 2 4 6 8 10 X 12 14 16 18 20 r = 0. 942 20 0 0 2 4 6 16 16 14 14 12 12 10 10 10 X 12 14 16 18 20 y y 18 8 r=0 20 18 8 8 6 6 4 4 2 2 0 r≐ 0 20 0 2 4 6 8 10 X 12 14 16 18 20 0 0 2 4 6 8 Chapter 2: DESCRIPTIVE STATISTICS – PART II 10 X 12 14 16 18 20 10

Correlation (continued) � Chapter 2: DESCRIPTIVE STATISTICS – PART II 11

Regression Models � Chapter 2: DESCRIPTIVE STATISTICS – PART II 12

Regression Models (continued) � 18 18 16 16 14 14 12 12 10 10 y 20 8 8 6 6 4 4 2 2 0 0 2 4 6 8 10 X 12 14 16 18 20 0 0 2 4 6 8 Chapter 2: DESCRIPTIVE STATISTICS – PART II 10 X 12 14 16 18 20 13

Simple Linear Regression Model � Chapter 2: DESCRIPTIVE STATISTICS – PART II 14

The Method of Least Squares � Chapter 2: DESCRIPTIVE STATISTICS – PART II 15

The Method of Least Squares (continued) � Chapter 2: DESCRIPTIVE STATISTICS – PART II 16

The Method of Least Squares (continued) � Chapter 2: DESCRIPTIVE STATISTICS – PART II 17

How Can We Interpret Regression Coefficients? � Chapter 2: DESCRIPTIVE STATISTICS – PART II 18

Goodness of Fit of a Regression Model � Chapter 2: DESCRIPTIVE STATISTICS – PART II 19

Goodness of Fit of a Regression Model (continued) � Chapter 2: DESCRIPTIVE STATISTICS – PART II 20

Coefficient of Determination � Chapter 2: DESCRIPTIVE STATISTICS – PART II 21

Example � Chapter 2: DESCRIPTIVE STATISTICS – PART II 22