7/17/2019 Lecture 07 - Regression Analysis 1

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Advanced Mathematics for

Business

Topic 7:

Regression Analysis 1

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Regression Analysis 1 Topic 7 - 1.2

Scope and Coverage

This topic will cover:

Simple linear regression

Pearsons (product moment) correlation coefficient

Spearmans (rank order) correlation coefficient

7/17/2019 Lecture 07 - Regression Analysis 1

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Regression Analysis 1 Topic 7 - 1.

earning !utcomes

By the end of this topic students will be able to:

"nderstand a straight line fit to #ivariate data

Calculate and interpret Pearsons correlation

coefficient

Calculate and interpret Spearmans correlation

coefficient

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Regression Analysis 1 Topic 7 - 1.!

Motivation

$he search for% and strength of% predictors

& 'hat is a good predictor of future o# performance

& 'hat is this products price&demand curve

& 'hich process factors affect production *ield

& +o, does a particular share price move ,ith the

market average

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Regression Analysis 1 Topic 7 - 1."

$he inear -elationship

income

savings

x

y

x

yy. mx/ c

Assuming interval or ratio data0

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Regression Analysis 1 Topic 7 - 1.#

east SS1 -egression Criterion & 2

x

y e3

e2

e4

e5e6

7/17/2019 Lecture 07 - Regression Analysis 1

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Regression Analysis 1 Topic 7 - 1.7

east SS1 -egression Criterion & 4

x

y e3

e2

e4

e5e6

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Regression Analysis 1 Topic 7 - 1.$

east SS1 -egression Criterion & 5

7/17/2019 Lecture 07 - Regression Analysis 1

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Regression Analysis 1 Topic 7 - 1.%

17ample & 2

A compan* has #een carr*ing out e7periments ,iththe position of a #utton on its ,e#site0

Page

Position(% vertical)

Click

Throughs(%)

43 5089

38 30:6

93 ;0:5

288 2804:

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Regression Analysis 1 Topic 7 - 1.10

17ample & 4

A compan* has #een carr*ing out e7periments ,iththe position of a #utton on its ,e#site0

x y xy x2

43 5089 9:093 :43

38 30:6 4

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Regression Analysis 1 Topic 7 - 1.11

17ample & 5

A compan* has #een carr*ing out e7periments ,ith

the position of a #utton on its ,e#site0

PagePosition

(% vertical)

ClickThroughs

(%)

43 5089

38 30:6

93 ;0:5

288 2804:

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Regression Analysis 1 Topic 7 - 1.12

17ercise & 2

A compan* has #een carr*ing out e7periments ,ith

the position of a #utton on its ,e#site0

x y xy x2

43 2066 3

38 303< 4388

93 260:6 3:43

288 :0;6 28888

total 250 18750

mean 62.5

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Regression Analysis 1 Topic 7 - 1.1

17ercise & 4

A compan* has #een carr*ing out e7periments ,ith

the position of a #utton on its ,e#site0

x y xy x2

43 2066 5: 3

38 303< 49; 4388

93 260:6 28;< 3:43

288 :0;6 :;6 28888

total 250 28.6 2107 18750

mean 62.5 7.15

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Regression Analysis 1 Topic 7 - 1.1!

+o, 'ell =oes the ine >it & 2

x y

43 2066

38 303