Vectors I

Correlation & RegressionE-Learning Module

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Bivariate DataScatter DiagramsIndependent & Dependent VariablesLinear RegressionProduct Moment Correlation CoefficientInterpolation & ExtrapolationReliability of EstimatesLinearisation of Data

Overview

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comprises the values of two variablesis obtained from the same sample

Bivariate Data

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Amount of advertising time for a product and number of sales for that productHeights of persons and their agesMathematics test scores and English test scores

Bivariate Data (Examples)

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A plot of a set of bivariate data in the x y plane

Scatter Diagrams

x (%)y (%)O

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Independent variable: the variable whose values are controlledDependent variable: the variable whose values are influenced by or vary with changes in values of the independent variableIndependent & Dependent Variables

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A set of bivariate data between two variables X and Y is given as follows.

X2545607590Y8872574423

(i)Sketch a scatter diagram for this set of data.(ii)Using the scatter diagram, describe a possible relationship between the two variables X and Y.

Example 1.1

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(iii)Explain whether the relationship you have observed in part (ii) suggests that one directly causes the other.(iv)If X and Y represent the following variables, state whether or not one variable depends on the other, and identify the independent and dependent variables when it does.(a) Time passed (X), concentration of a substance in a solution (Y)(b) Temperature (X), Wind speed (Y)(c) Mathematics Test scores (X), English Test scores (Y)

Example 1.1 (contd)

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Example 1.1 (i)

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Example 1.1 (i) (contd)

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