Part 5 Statistical Models for Forecasting and Planning

12. 1 Introduction In management, many numeric measures are related (either strongly or loosely)

Introduction cont’d • the number of hours of operator training is believed to impact

Scatter plot between pairs of x and y © Juta and Company Ltd, 2012

Simple Linear Regression Analysis Simple linear regression analysis finds a straightline equation that represents

Relationships between sets of numeric random variables © Juta and Company Ltd, 2012 Applied

© Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3

Correlation Analysis The reliability of the estimate of y depends on the strength of

Correlation Analysis cont’d • This measure is called Pearson’s correlation coefficient. It is represented

How to interpret a Correlation Coefficient © Juta and Company Ltd, 2012 Applied Business

Perfect associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based

Strong associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based

Moderate to weak associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods

No association © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based

Compare the sample test statistic to the region of acceptance © Juta and Company

Summary Output © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based

Superimposed regression equation © Juta and Company Ltd, 2012 Applied Business Statistics Methods and

• Summary • Exercises © Juta and Company Ltd, 2012 Applied Business Statistics

End of Chapter 12 Applied Business Statistics Methods and Excel-based Applications Third edition TREVOR

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Part 5 Statistical Models for Forecasting and Planning Chapter 12 Simple Linear Regression and Correlation Analysis © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 1

12. 1 Introduction In management, many numeric measures are related (either strongly or loosely) to one another. For example: • advertising expenditure is assumed to influence sales volumes; • a company’s share price is likely to be influenced by its return on investment; © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 2

Introduction cont’d • the number of hours of operator training is believed to impact positively on productivity; and • the operating speed of a bottling machine affects the reject rate of under-filled bottles. © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 3

Scatter plot between pairs of x and y © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 4

Simple Linear Regression Analysis Simple linear regression analysis finds a straightline equation that represents the relationship between the values of two numeric variables. © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 5

Relationships between sets of numeric random variables © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 6

Correlation Analysis The reliability of the estimate of y depends on the strength of the relationship between the x and y variables. A strong relationship implies a more accurate and reliable estimate of y. • Correlation analysis measures the strength of the linear association between two numeric • (ratio-scaled) variables, x and y. © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 11

Correlation Analysis cont’d • This measure is called Pearson’s correlation coefficient. It is represented by the symbol r • when it is calculated from sample data. • The following formula is used to calculate the sample correlation coefficient: © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 12

How to interpret a Correlation Coefficient © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 13

Perfect associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 14

Strong associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 15

Moderate to weak associations © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 16

No association © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 17

Compare the sample test statistic to the region of acceptance © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 20

Summary Output © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 21

Superimposed regression equation © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 22

• Summary • Exercises © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 23

End of Chapter 12 Applied Business Statistics Methods and Excel-based Applications Third edition TREVOR WEGNER ISBN 978 -0 -70217 -774 -3 © Juta and Company Ltd, 2012 Applied Business Statistics Methods and Excel-Based Applications 3 rd Edition 24