Business statistics: for non-mathematicians
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Palgrave Macmillan
2007
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis Klappentext |
| Physical Description: | XVI, 368 S. graph. Darst. |
| ISBN: | 9780230506466 0230506461 |
Staff View
MARC
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| 245 | 1 | 0 | |a Business statistics |b for non-mathematicians |c Sonia Taylor |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Palgrave Macmillan |c 2007 | |
| 300 | |a XVI, 368 S. |b graph. Darst. | ||
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| adam_text | Contents
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Preface xiii
11ntroduction to statistics 1
Objectives of this chapter 1
1.1 What do we mean by statistics? 2
1.2 Why do we need statistics? 2
1.3 Types of data and scales of measurement 3
1.3.1 Categorical data 3
1.3.2 Interval and ratio data 4
1.3.3 Qualitative and quantitative data 5
1.3.4 Discrete and continuous data 5
1.4 Populations and samples 5
1.5 Descriptive statistics 6
1.6 Inferential statistics 6
1.7 Summary 6
1.8 Case study 7
1.8.1 Scenario 7
1.8.2 The data 8
1.9 Check your course prerequisites 8
Tutorial 1: Basic mathematics revision 9
2 Graphical representation of data 11
Objectives of this chapter 11
2.1 Introduction: why do we represent data by graphs? 12
2.2 Tabulation 12
2.3 Graphs of non-metric (non-measurable) data 13
2.3.1 Bar charts 13
2.3.2 Pie charts 15
2.3.3 Pictograms 15
VI
Contents
2.4 Graphs of metric (measurable) data 16
2.4.1 Histograms 16
2.4.2 Frequency polygons 19
2.4.3 Stem-and-leaf plots 20
2.4.4 Dot plots 22
2.4.5 Cumulative frequency polygons (ogives) 22
2.4.6 Box plots 25
2.5 A continuous example using graphics 26
2.6 Interpretation of published graphs 31
2.7 Further methods of graphical description 32
2.8 Summary 32
2.9 Case study (see Section 1.8 for background information) 32
Tutorial 2: Graphical presentation 33
3 Numerical summary of data
35
Objectives of this chapter
3.1 Introduction: why do we need to summarise data numerically?
3.2 Measures of centrality (location)
3.2.1 The mode
3.2.2 The median
3.2.3 The mean
3.3 Measures of spread
3.3.1 Range
3.3.2 Interquartile range
3.3.3 Standard deviation
3.4 Estimation of summary statistics from graphs
3.4.1 Estimating the mode from a histogram
3.4.2 Estimating the median, quartiles and interquartile range from an ogive
3.5 Other summary statistics
3.5.1 Centrality
3.5.2 Spread
3.5.3 Skewness
3.6 Computer numerical summary of Example 3.1
3.7 Summary
3.8 Case study
3.9 Calculator practice Tutorial 3: Data summary
35
36 36 36
36
37 41 41
41
42 49
49
50 52 52
52
53
53
54
55 55 57
4 Probability 59
Objectives of this chapter 59
4.1 Introduction: the role of probability in statistics 60
4.2 Probability as a measure of uncertainty 61
4.2.1 Measures of uncertainty 61
4.2.2 Value of probability 61
4.2.3 Assessing probability 61
4.3 Probability from symmetry 62
4.3.1 Combining independent probabilities 64
Contents vii
4.4 Probability from relative frequency 66
4.4.1 Estimating probability from long-term relative frequency 66
4.4.2 Estimating probability from frequency tables 67
4.4.3 Estimating probability from histograms 68
4.5 Probabilities from contingency tables 69
4.6 Conditional probability 71
4.6.1 Tree diagrams 73
4.7 Expected values 76
4.8 Further work with probability 78
4.9 Summary 79
Tutorial 4: Probability 79
5 Normal distribution 82
Objectives of this chapter 82
5.1 Introduction: importance of the normal distribution 83
5.2 The characteristics of any normal distribution 83
5.2.1 The area beneath the normal distribution curve 84
5.3 The standardised normal distribution 85
5.4 Finding probabilities under a normal curve 85
5.5 Finding values from given proportions 90
5.6 Further applications of the normal distribution 94
5.7 A brief look at other probability distributions 94
5.7.1 Binomial distribution 95
5.7.2 Poisson distribution 96
5.7.3 (Negative) exponential distribution 97
5.8 Summary 98
5.9 Case study 98
Tutorial 5: Normal distribution 99
6 Estimation 102
Objectives of this chapter 102
6.1 Why can t we find the exact answer? 103
6.2 Taking a sample 103
6.2.1 Simple random sampling 104
6.2.2 Systematic sampling 104
6.2.3 Stratified random sampling 104
6.2.4 Cluster sampling 105
6.2.5 Multi-stage sampling 105
6.2.6 Quota sampling 105
6.3 Point and interval estimates 105
6.3.1 Point estimate 105
6.3.2 Interval estimate (confidence interval) 106
6.4 Confidence intervals for a percentage or proportion 106
6.5 Confidence intervals for one mean 108
6.5.1 Estimation of population mean when a is known 110
6.5.2 Estimation of population mean for large sample size and a unknown 110
6.5.3 Estimation of population mean for small sample size and o unknown 111
6.6 Confidence intervals for two independent means 112
Contents
viii
6 7 Confidence intervals for paired data 113
6 8 A continuous example using confidence intervals 114
6.9 Interpretation of confidence intervals 116
6. lOFurther applications of estimations 117
6.11 Computer analysis of Examples 6.6 and 6.8 117
6.12 Summary 119
6.13 Case study 120
Tutorial 6: Confidence intervals 120
7 Hypothesis testing 123
Objectives of this chapter 123
7.1 General concept of hypothesis testing 124
7.2 Common methodology 124
7.3 Testing for percentages or proportions 126
7.4 Testing for one mean 128
7.4.1 Method of testing for one mean 129
7.4.2 Testing for one mean when a is known 130
7.4.3 Testing for one mean when a is not known and the sample is large 131
7.4.4 Testing for one mean when o is not known and the sample is small
- one sample t-test 132
7.5 Testing for two independent means 133
7.5.1 Testing the difference between two means - c1? G2 known 133
7.5.2 Testing the difference between two means - Gp o2 unknown
- two-sample t-test 134
7.6 Testing for means of paired data 136
7.6.1 Hypothesis test for mean of differences of paired data - paired t-test 136
7.7 A continuous example using hypothesis testing 138
7.8 Non-parametric tests 141
7.8.1 The sign test 141
7.8.2 Wilcoxon matched pairs (signed rank) test 142
7.8.3 Mann-Whitney U test (Wilcoxon rank sum test) 143
7.9 Other hypothesis tests 145
7.10 Further considerations 145
7.10.1 Types of error 146
7.10.2 The power of a test 146
7.10.3 The validity of a test 146
7.11 Summary 148
7.12 Computer output for Example 7.9 148
7.13 Case study 151
Tutorial 7: Hypothesis testing 151
8 Analysis of variance 154
Objectives of this chapter 154
8.1 Introduction - why do we need analysis of variance? 155
8.2 One-way analysis of variance 155
8.2.1 Assumptions needed to be met for ANOVA 155
8.2.2 The one-way AN OVA model 156
Contents
IX
8.2.3 Sums of squares as a measure of deviation from the mean 156
8.2.4 ANOVA table 158
8.2.5 The hypothesis test 159
8.2.6 Where does any significant difference lie? 159
8.3 Two-way analysis of variance 161
8.3.1 Randomised block design 162
8.3.2 Main effects only 164
8.3.3 Main effects and interactions 168
8.4 Further analysis using ANOVA techniques 168
8.4.1 Factorial model 169
8.4.2 Latin square model 171
8.5 A continuous example using ANOVA 173
8.6 The Kruskal-Wallis test 177
8.7 Summary of analysis of variance (ANOVA) 178
8.8 Computer analysis of Examples 8.1, 8.3 and 8.5 178
8.9 Case study 183
Tutorial 8: analysis of variance 183
9 Correlation and regression 186
Objectives of this chapter 186
9.1 Introduction 187
9.2 Scatter diagrams 188
9.2.1 Independent and dependent variable 188
9.3 Pearson’s product moment correlation coefficient 190
9.3.1 Calculation of Pearson’s correlation coefficient 190
9.3.2 Hypothesis test for Pearson’s correlation coefficient 191
9.4 Regression equation (least squares) 192
9.4.1 Interpretation of regression equation 193
9.5 Goodness of fit 194
9.6 Using the regression model for prediction or estimation 194
9.6.1 Precision of predictions 195
9.7 Residual analysis 196
9.8 A continuous example using correlation and regression 197
9.9 Spearman’s rank correlation coefficient 200
9.9.1 Calculation of Spearman’s rank correlation coefficient 200
9.9.2 Hypothesis test for a Spearman’s correlation coefficient 201
9.10 Further methods and applications of regression 202
9.10.1 Non-linear regression 202
9.10.2 Multiple regression 203
9.10.3 Log-linear regression 203
9.11 Summary 203
9.12 Computer output for regression - Example 9.1 203
9.13 Case study 205
9.14 Calculator use and practice for regression 206
9.14.1 Practice 206
9.15 Use of formulae for calculating correlation and regression coefficients 207
9.15.1 Pearson’s product moment correlation coefficient 207
9.15.2 Regression equation 207
Tutorial 9: correlation and regression 209
X
Contents
I o Contingency tables and chi-square test 212
Objectives of this chapter 212
10.1 Introduction 213
10.2 Contingency tables (cross-tabs) 213
10.3 Chi-square (X2) test for independence 214
10.3.1 Expected values 214
10.3.2 The chi-square (X2) hypothesis test 216
10.4 Chi-square (X2) test for independence - 2 by 2 tables 217
10.5 Chi-square test for goodness of fit 219
10.6 A continuous chi-square test for independence 220
10.7 Further analysis of categorical data 222
10.8 Summary 223
10.9 Computer output for chi-square tests - Example 10.1 223
10.10 Case study 225
Tutorial 10: Chi-square test 225
II Index numbers 227
Objectives of this chapter 227
11TIntroduction: measuring changes over time. 228
11.2 Index numbers 228
11.2.1 Price indices 229
11.2.2 The Retail Price Index - the RPI 229
11.2.3 Quantity indices 229
11.3 Simple indices 230
11.4 Calculating changes 231
11.4.1 Percentage point change 231
11.4.2 Percentage change 232
11.5 Changing the base period 233
11.6 Comparing time series 234
11.7 Deflating an index 236
11.8 Simple aggregate indices 237
11.8.1 Aggregate price index 237
11.8.2 Aggregate quantity index 238
11.9 Weighted aggregate indices 238
11.9.1 The Laspeyre base-weighted index 239
11.9.2 The Paasche current-weighted index 240
11.9.3 The Fisher index 241
11.10 A continuous example using index numbers 241
11.11 Summary 246
11.12 Case study 246
Tutorial 11: index numbers 246
12 Time series 249
Objectives of this chapter 249
12.1 Introduction: inspection of a time series 250
12.2 Non-seasonal time series 251
Contents
XI
12.2.1 Time series plot 251
12.2.2 Regression models 252
12.2.3 Exponential smoothing models 253
12.3 A continuous example of non-seasonal modelling 256
12.4 Decomposition of seasonal time series 258
12.4.1 Additive model - by calculation and graph 258
12.4.2 Additive model by computer package 263
12.4.3 Multiplicative model by computer package 264
12.4.4 Seasonal effects and deseasonalised values 265
12.5 Residual analysis 266
12.6 Further analysis of time series 272
12.7 Summary 273
12.7.1 Method summary 273
Tutorial 12: Time series analysis 275
13. Forecasting 278
Objectives of this chapter 278
13.1 Introduction: the importance of forecasting 279
13.2 Forecasts 279
13.3 Forecasting with a non-seasonal time series model 279
13.4 A further non-seasonal time series forecast 282
13.5 Forecasting with a seasonal model 283
13.5.1 Additive model 284
13.5.2 Multiplicative model 286
13.6 How good is a forecast? 287
13.7 Further methods of forecasting 290
13.8 Summary 291
Tutorial 13: forecasting 291
14 Computer analysis 293
14.1 Introduction to SPSS 293
14.2 SPSS worksheets 296
14.2.1 Graphical presentation with SPSS 296
14.2.2 Summary statistics with SPSS 300
14.2.3 Estimation and hypothesis testing with SPSS 302
14.2.4 Analysis of variance with SPSS 303
14.2.5 Correlation and regression analysis with SPSS 305
14.2.6 Time series analysis and forecasting with SPSS 306
14.3 Numerical answers to SPSS worksheets 308
14.2.1 Graphical presentation 308
14.2.2 Summary statistics 308
14.2.3 Estimation and hypothesis testing 308
14.2.4 Analysis of variance 308
14.2.5 Correlation and regression analysis 309
14.2.6 Time series analysis and forecasting 309
14.4 Introduction to Minitab 309
14.5 Minitab worksheets 310
Contents
xii
14.5.1 Graphical presentation with Minitab 310
14.5.2 Summary statistics with Minitab 314
14.5.3 Estimation and hypothesis testing with with Minitab 315
14.5.4 Analysis of variance with Minitab 317
14.5.5 Correlation and regression with Minitab 318
14.5.6 Time series analysis and forecasting with Minitab 319
14.6 Numerical answers to Minitab worksheets 321
14.5.1 Graphical presentation 321
14.5.2 Summary statistics 321
14.5.3 Estimation and hypothesis testing 321
14.5.4 Analysis of variance 322
14.5.5 Correlation and regression analysis 322
14.5.6 Time series analysis and forecasting 322
14.7 Introduction to Excel 322
14.8 Excel worksheets 323
14.8.1 Graphical presentation with Excel. 323
14.8.2 Summary statistics with Excel 326
14.8.3 Estimation and hypothesis testing with Excel 327
14.8.4 Analysis of variance with Excel 329
14.8.5 Correlation and regression with Excel 330
14.8.6 Time series analysis and forecasting with Excel 331
14.9 Numerical answers to Excel worksheets 332
14.8.1 Graphical presentation 332
14.8.2 Summary statistics 332
14.8.3 Estimation and hypothesis testing 332
14.8.4 Analysis of variance 333
14.8.5 Correlation and regression 333
14.8.6 l ime series analysis and forecasting 333
Appendix 334
A Answers to tutorial questions 334
B Glossary of terms 340
C Notation and formulae 346
Greek alphabet 346
Notation 346
Formulae 346
D Tables 350
E Students’ materials on the companion website 360
F Lecturers’ materials on the companion website 360
G References 361
Index
362
|
| adam_txt |
Contents
11*81
:Kv . ' . ■ ' J i
■ -1 : : ; :: v:-
’: ::::
. - • v: • •• - f ,i«= i
ilidilS -•••!;
Ipiii
ill
. ;
:S;
•i::.
Preface xiii
11ntroduction to statistics 1
Objectives of this chapter 1
1.1 What do we mean by statistics? 2
1.2 Why do we need statistics? 2
1.3 Types of data and scales of measurement 3
1.3.1 Categorical data 3
1.3.2 Interval and ratio data 4
1.3.3 Qualitative and quantitative data 5
1.3.4 Discrete and continuous data 5
1.4 Populations and samples 5
1.5 Descriptive statistics 6
1.6 Inferential statistics 6
1.7 Summary 6
1.8 Case study 7
1.8.1 Scenario 7
1.8.2 The data 8
1.9 Check your course prerequisites 8
Tutorial 1: Basic mathematics revision 9
2 Graphical representation of data 11
Objectives of this chapter 11
2.1 Introduction: why do we represent data by graphs? 12
2.2 Tabulation 12
2.3 Graphs of non-metric (non-measurable) data 13
2.3.1 Bar charts 13
2.3.2 Pie charts 15
2.3.3 Pictograms 15
VI
Contents
2.4 Graphs of metric (measurable) data 16
2.4.1 Histograms 16
2.4.2 Frequency polygons 19
2.4.3 Stem-and-leaf plots 20
2.4.4 Dot plots 22
2.4.5 Cumulative frequency polygons (ogives) 22
2.4.6 Box plots 25
2.5 A continuous example using graphics 26
2.6 Interpretation of published graphs 31
2.7 Further methods of graphical description 32
2.8 Summary 32
2.9 Case study (see Section 1.8 for background information) 32
Tutorial 2: Graphical presentation 33
3 Numerical summary of data
35
Objectives of this chapter
3.1 Introduction: why do we need to summarise data numerically?
3.2 Measures of centrality (location)
3.2.1 The mode
3.2.2 The median
3.2.3 The mean
3.3 Measures of spread
3.3.1 Range
3.3.2 Interquartile range
3.3.3 Standard deviation
3.4 Estimation of summary statistics from graphs
3.4.1 Estimating the mode from a histogram
3.4.2 Estimating the median, quartiles and interquartile range from an ogive
3.5 Other summary statistics
3.5.1 Centrality
3.5.2 Spread
3.5.3 Skewness
3.6 Computer numerical summary of Example 3.1
3.7 Summary
3.8 Case study
3.9 Calculator practice Tutorial 3: Data summary
35
36 36 36
36
37 41 41
41
42 49
49
50 52 52
52
53
53
54
55 55 57
4 Probability 59
Objectives of this chapter 59
4.1 Introduction: the role of probability in statistics 60
4.2 Probability as a measure of uncertainty 61
4.2.1 Measures of uncertainty 61
4.2.2 Value of probability 61
4.2.3 Assessing probability 61
4.3 Probability from symmetry 62
4.3.1 Combining independent probabilities 64
Contents vii
4.4 Probability from relative frequency 66
4.4.1 Estimating probability from long-term relative frequency 66
4.4.2 Estimating probability from frequency tables 67
4.4.3 Estimating probability from histograms 68
4.5 Probabilities from contingency tables 69
4.6 Conditional probability 71
4.6.1 Tree diagrams 73
4.7 Expected values 76
4.8 Further work with probability 78
4.9 Summary 79
Tutorial 4: Probability 79
5 Normal distribution 82
Objectives of this chapter 82
5.1 Introduction: importance of the normal distribution 83
5.2 The characteristics of any normal distribution 83
5.2.1 The area beneath the normal distribution curve 84
5.3 The standardised normal distribution 85
5.4 Finding probabilities under a normal curve 85
5.5 Finding values from given proportions 90
5.6 Further applications of the normal distribution 94
5.7 A brief look at other probability distributions 94
5.7.1 Binomial distribution 95
5.7.2 Poisson distribution 96
5.7.3 (Negative) exponential distribution 97
5.8 Summary 98
5.9 Case study 98
Tutorial 5: Normal distribution 99
6 Estimation 102
Objectives of this chapter 102
6.1 Why can t we find the exact answer? 103
6.2 Taking a sample 103
6.2.1 Simple random sampling 104
6.2.2 Systematic sampling 104
6.2.3 Stratified random sampling 104
6.2.4 Cluster sampling 105
6.2.5 Multi-stage sampling 105
6.2.6 Quota sampling 105
6.3 Point and interval estimates 105
6.3.1 Point estimate 105
6.3.2 Interval estimate (confidence interval) 106
6.4 Confidence intervals for a percentage or proportion 106
6.5 Confidence intervals for one mean 108
6.5.1 Estimation of population mean when a is known 110
6.5.2 Estimation of population mean for large sample size and a unknown 110
6.5.3 Estimation of population mean for small sample size and o unknown 111
6.6 Confidence intervals for two independent means 112
Contents
viii
6 7 Confidence intervals for paired data 113
6 8 A continuous example using confidence intervals 114
6.9 Interpretation of confidence intervals 116
6. lOFurther applications of estimations 117
6.11 Computer analysis of Examples 6.6 and 6.8 117
6.12 Summary 119
6.13 Case study 120
Tutorial 6: Confidence intervals 120
7 Hypothesis testing 123
Objectives of this chapter 123
7.1 General concept of hypothesis testing 124
7.2 Common methodology 124
7.3 Testing for percentages or proportions 126
7.4 Testing for one mean 128
7.4.1 Method of testing for one mean 129
7.4.2 Testing for one mean when a is known 130
7.4.3 Testing for one mean when a is not known and the sample is large 131
7.4.4 Testing for one mean when o is not known and the sample is small
- one sample t-test 132
7.5 Testing for two independent means 133
7.5.1 Testing the difference between two means - c1? G2 known 133
7.5.2 Testing the difference between two means - Gp o2 unknown
- two-sample t-test 134
7.6 Testing for means of paired data 136
7.6.1 Hypothesis test for mean of differences of paired data - paired t-test 136
7.7 A continuous example using hypothesis testing 138
7.8 Non-parametric tests 141
7.8.1 The sign test 141
7.8.2 Wilcoxon matched pairs (signed rank) test 142
7.8.3 Mann-Whitney U test (Wilcoxon rank sum test) 143
7.9 Other hypothesis tests 145
7.10 Further considerations 145
7.10.1 Types of error 146
7.10.2 The power of a test 146
7.10.3 The validity of a test 146
7.11 Summary 148
7.12 Computer output for Example 7.9 148
7.13 Case study 151
Tutorial 7: Hypothesis testing 151
8 Analysis of variance 154
Objectives of this chapter 154
8.1 Introduction - why do we need analysis of variance? 155
8.2 One-way analysis of variance 155
8.2.1 Assumptions needed to be met for ANOVA 155
8.2.2 The one-way AN OVA model 156
Contents
IX
8.2.3 Sums of squares as a measure of deviation from the mean 156
8.2.4 ANOVA table 158
8.2.5 The hypothesis test 159
8.2.6 Where does any significant difference lie? 159
8.3 Two-way analysis of variance 161
8.3.1 Randomised block design 162
8.3.2 Main effects only 164
8.3.3 Main effects and interactions 168
8.4 Further analysis using ANOVA techniques 168
8.4.1 Factorial model 169
8.4.2 Latin square model 171
8.5 A continuous example using ANOVA 173
8.6 The Kruskal-Wallis test 177
8.7 Summary of analysis of variance (ANOVA) 178
8.8 Computer analysis of Examples 8.1, 8.3 and 8.5 178
8.9 Case study 183
Tutorial 8: analysis of variance 183
9 Correlation and regression 186
Objectives of this chapter 186
9.1 Introduction 187
9.2 Scatter diagrams 188
9.2.1 Independent and dependent variable 188
9.3 Pearson’s product moment correlation coefficient 190
9.3.1 Calculation of Pearson’s correlation coefficient 190
9.3.2 Hypothesis test for Pearson’s correlation coefficient 191
9.4 Regression equation (least squares) 192
9.4.1 Interpretation of regression equation 193
9.5 Goodness of fit 194
9.6 Using the regression model for prediction or estimation 194
9.6.1 Precision of predictions 195
9.7 Residual analysis 196
9.8 A continuous example using correlation and regression 197
9.9 Spearman’s rank correlation coefficient 200
9.9.1 Calculation of Spearman’s rank correlation coefficient 200
9.9.2 Hypothesis test for a Spearman’s correlation coefficient 201
9.10 Further methods and applications of regression 202
9.10.1 Non-linear regression 202
9.10.2 Multiple regression 203
9.10.3 Log-linear regression 203
9.11 Summary 203
9.12 Computer output for regression - Example 9.1 203
9.13 Case study 205
9.14 Calculator use and practice for regression 206
9.14.1 Practice 206
9.15 Use of formulae for calculating correlation and regression coefficients 207
9.15.1 Pearson’s product moment correlation coefficient 207
9.15.2 Regression equation 207
Tutorial 9: correlation and regression 209
X
Contents
I o Contingency tables and chi-square test 212
Objectives of this chapter 212
10.1 Introduction 213
10.2 Contingency tables (cross-tabs) 213
10.3 Chi-square (X2) test for independence 214
10.3.1 Expected values 214
10.3.2 The chi-square (X2) hypothesis test 216
10.4 Chi-square (X2) test for independence - 2 by 2 tables 217
10.5 Chi-square test for goodness of fit 219
10.6 A continuous chi-square test for independence 220
10.7 Further analysis of categorical data 222
10.8 Summary 223
10.9 Computer output for chi-square tests - Example 10.1 223
10.10 Case study 225
Tutorial 10: Chi-square test 225
II Index numbers 227
Objectives of this chapter 227
11TIntroduction: measuring changes over time. 228
11.2 Index numbers 228
11.2.1 Price indices 229
11.2.2 The Retail Price Index - the RPI 229
11.2.3 Quantity indices 229
11.3 Simple indices 230
11.4 Calculating changes 231
11.4.1 Percentage point change 231
11.4.2 Percentage change 232
11.5 Changing the base period 233
11.6 Comparing time series 234
11.7 Deflating an index 236
11.8 Simple aggregate indices 237
11.8.1 Aggregate price index 237
11.8.2 Aggregate quantity index 238
11.9 Weighted aggregate indices 238
11.9.1 The Laspeyre base-weighted index 239
11.9.2 The Paasche current-weighted index 240
11.9.3 The Fisher index 241
11.10 A continuous example using index numbers 241
11.11 Summary 246
11.12 Case study 246
Tutorial 11: index numbers 246
12 Time series 249
Objectives of this chapter 249
12.1 Introduction: inspection of a time series 250
12.2 Non-seasonal time series 251
Contents
XI
12.2.1 Time series plot 251
12.2.2 Regression models 252
12.2.3 Exponential smoothing models 253
12.3 A continuous example of non-seasonal modelling 256
12.4 Decomposition of seasonal time series 258
12.4.1 Additive model - by calculation and graph 258
12.4.2 Additive model by computer package 263
12.4.3 Multiplicative model by computer package 264
12.4.4 Seasonal effects and deseasonalised values 265
12.5 Residual analysis 266
12.6 Further analysis of time series 272
12.7 Summary 273
12.7.1 Method summary 273
Tutorial 12: Time series analysis 275
13. Forecasting 278
Objectives of this chapter 278
13.1 Introduction: the importance of forecasting 279
13.2 Forecasts 279
13.3 Forecasting with a non-seasonal time series model 279
13.4 A further non-seasonal time series forecast 282
13.5 Forecasting with a seasonal model 283
13.5.1 Additive model 284
13.5.2 Multiplicative model 286
13.6 How good is a forecast? 287
13.7 Further methods of forecasting 290
13.8 Summary 291
Tutorial 13: forecasting 291
14 Computer analysis 293
14.1 Introduction to SPSS 293
14.2 SPSS worksheets 296
14.2.1 Graphical presentation with SPSS 296
14.2.2 Summary statistics with SPSS 300
14.2.3 Estimation and hypothesis testing with SPSS 302
14.2.4 Analysis of variance with SPSS 303
14.2.5 Correlation and regression analysis with SPSS 305
14.2.6 Time series analysis and forecasting with SPSS 306
14.3 Numerical answers to SPSS worksheets 308
14.2.1 Graphical presentation 308
14.2.2 Summary statistics 308
14.2.3 Estimation and hypothesis testing 308
14.2.4 Analysis of variance 308
14.2.5 Correlation and regression analysis 309
14.2.6 Time series analysis and forecasting 309
14.4 Introduction to Minitab 309
14.5 Minitab worksheets 310
Contents
xii
14.5.1 Graphical presentation with Minitab 310
14.5.2 Summary statistics with Minitab 314
14.5.3 Estimation and hypothesis testing with with Minitab 315
14.5.4 Analysis of variance with Minitab 317
14.5.5 Correlation and regression with Minitab 318
14.5.6 Time series analysis and forecasting with Minitab 319
14.6 Numerical answers to Minitab worksheets 321
14.5.1 Graphical presentation 321
14.5.2 Summary statistics 321
14.5.3 Estimation and hypothesis testing 321
14.5.4 Analysis of variance 322
14.5.5 Correlation and regression analysis 322
14.5.6 Time series analysis and forecasting 322
14.7 Introduction to Excel 322
14.8 Excel worksheets 323
14.8.1 Graphical presentation with Excel. 323
14.8.2 Summary statistics with Excel 326
14.8.3 Estimation and hypothesis testing with Excel 327
14.8.4 Analysis of variance with Excel 329
14.8.5 Correlation and regression with Excel 330
14.8.6 Time series analysis and forecasting with Excel 331
14.9 Numerical answers to Excel worksheets 332
14.8.1 Graphical presentation 332
14.8.2 Summary statistics 332
14.8.3 Estimation and hypothesis testing 332
14.8.4 Analysis of variance 333
14.8.5 Correlation and regression 333
14.8.6 l ime series analysis and forecasting 333
Appendix 334
A Answers to tutorial questions 334
B Glossary of terms 340
C Notation and formulae 346
Greek alphabet 346
Notation 346
Formulae 346
D Tables 350
E Students’ materials on the companion website 360
F Lecturers’ materials on the companion website 360
G References 361
Index
362
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