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Section 3.1-3.2

# Section 3.1-3.2 - Chapter 3 Bivariate Data and...

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Chapter 3 Bivariate Data and Distributions So far , we discussed the methods for analyzing univariate data. Now we discuss multivariate data, obtained simultaneously on more than one variable. Our focus is mainly analyzing bivariate data obtained on two variables . and y x 3.1 Bivariate Data The data 1 1 ( , )...,( , ) n n x y x y obtained on two numerical variables x and y is called a bivariate data. For, example, let x = height of a student, y = weight of a student. The data of heights and weights of all students in a class constitute a bivariate data. The aim is investigate if the variables y x and are associated/correlated and the relationship is linear or non-linear. Scatter Plot Scatter plot is the graphical display of a bivariate data, taking i x - values along x - axis and i y - values along the y - axis. Just plot the points 1 1 ( , )...,( , ) n n x y x y . 1

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The resulting graph is called the Scatter Plot . Usually, x = explanatory (or independent) variable y = response (or dependent) variable Often we want to predict the response variable. Examine the scatter plot for the kind of association. (i) direction (negative or positive) (ii) Strength (no, moderate, strong) (iii) From (linear or not) (iv) Example 1: The following data represents the NO x emissions of 10 engines when baseline gasoline and reformulated gasoline were used. In the following example, x = age; 1 y = Emission of NO x (baseline gasoline); 2
y = Emission of NO x (reformulated gasoline). Engine: Age: Baseline: Reformulated: 1 0 1.72 1.88 2 0 4.38 5.93 3 2 4.06 5.54 4 11 1.26 2.67 5 7 5.31 6.53 6 16 0.57 0.74 7 9 3.37 4.94 8 0 3.44 4.89 9 12 0.74 0.69 10 4 1.24 1.42 The scatter plot is given below: Age: Y-Data 18 16 14 12 10 8 6 4 2 0 7 6 5 4 3 2 1 0 Variable Baseline: Reformulated: Scatterplot of Baseline:, Reformulated: vs Age: Example 2 Consider the following data on x =BOD mass loading and y = BOD mass removal. 3

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Section 3.1-3.2 - Chapter 3 Bivariate Data and...

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