Abercrombie & Fitch sales regression model
five-step evaluation model
dummy variables (RUEHL, Gilly Hicks), 153–157
personal income, 145–147
seasonal dummy variables, 150–153
unemployment rate, 147–150
hypothesis
dummy variables (RUEHL, Gilly Hicks), 145
personal income, 143–144
seasonal dummy variables, 144
unemployment rate, 144
Adjusted coefficient of determination, 84–851
Adjusted R-square, 84–85
AIC. See Akaike information criterion
Akaike information criterion (AIC), 177
Analysis of variance (ANOVA), 86, 187
Annual values for women’s clothing sales (AWCS), 28–29, 62–63
ANOVA. See Analysis of variance
Approximate 95% confidence interval estimate
college basketball winning percentage, 72–73
concept of, 66–68
market share multiple regression model, 103
multiple linear regression, 89
women’s clothing sales (WCS), 70–72
Bivariate linear regression (BLR) model, 24
Business applications, regression analysis
cross-sectional data, 2–3
time-series data, 3–4
Central tendency
mean, 184
median, 185
mode, 185
Cobb-Douglas production function, 136–137
Coefficient of determination
adjusted, 84–85
definition of, 50
development of, 174–176
College basketball winning percentage
actual vs. predicted values, 20
approximate 95% confidence interval estimate, 72–73
cross-sectional data, 18, 19
point estimate, 69
scatterplot, 19
Computed test statistic, 46, 49, 55, 81, 86
Confidence interval, 66–68
Constant. See Intercept
Correlation matrix
independent variables, 124
Miller’s Foods’ market share regression, 103
multicollinearity, 124
personal income, 153, 156
RUEHL and Gilly Hicks, 156
seasonal dummy variables, 153, 156
unemployment rate, 153, 156
Critical values
Durbin-Watson statistic, 60–61
F-distribution at 95% confidence level, 92–93
F-test, 86
hypothesis test, 45
Cross-sectional data, 2–3
Cubic functions, 130–134
Data Analysis
data tab, 9
in Excel 2003, 8
in Excel 2007, 8
in Excel 2010–2013, 9
OLS regression model in Excel, 32–37
Data types
interval data, 6–7
nominal data, 5
ordinal data, 5–6
ratio data, 7
Degrees of freedom, 58
Dependent variable, 24
Dispersion
range, 186
standard deviation, 186
standard error, 187
variance, 186–187
Dummy variables
Abercrombie & Fitch sales regression model
five-step evaluation model, 153–157
hypothesis, 145
definition of, 108
hypotheses, 120–121
multiple linear regression, 108–111
seasonality, 111–117
uses of, 108
women’s clothing sales, 111–117
Durbin-Watson (DW) statistic, 102
calculation in Excel, 62–64
critical values, 60–61
evaluation, 53
Explained variation, 175
Explanatory power of model
Abercrombie & Fitch sales
dummy variables, 155–156
personal income, 147
seasonal dummy variables, 152
unemployment rate, 163
market share multiple regression model, 101–102
multiple linear regression, 84–87
ordinary least squares (OLS) regression model, 50
Stoke’s Lodge occupancy, 55–56
Formal OLS regression model
alternative models, 179–181
mathematical approach of, 171–174
R-square development, 174–176
scattergram of Miller’s foods’ market share, 177–179
software programs
Akaike information criterion, 177
Schwarz criterion, 177
F-statistic, 86
Gilly Hicks, dummy variable
Abercrombie & Fitch sales, 153–157
correlation matrix, 156
hypothesis, 145
Homoscedasticity, 31
Hypothesis test, 43–50
Independent variable, 24
Intercept
basketball winning percentage, 26–27
definition of, 24–25
women’s clothing sales model, 25–26
Interval data, 6–7
Market share multiple regression model
approximate 95% confidence interval estimate, 103
explanatory power of model, 101–102
model does make sense?, 98–99
multicollinearity, 102–103
point estimate, 103–104
serial correlation, 102
statistical significance, 99–101
three-dimensional visual representation, 103–104
Mean, 184
Median, 185
Miller’s Foods’ market share. See also Market share multiple regression model
alternative models, 177
building and evaluating, 179–181
scattergram
advertising, 179
index of competitor’s advertising, 178
price, 178
Mode, 185
MONEYBALL, 18, 73
Monthly room occupancy (MRO)
actual and predicted values for, 119–120
function of gas price, 119
multiple linear regression, 77, 78
OLS regression models, 54
Stoke’s Lodge, 118
MRO. See Monthly room occupancy
Multicollinearity
Abercrombie & Fitch sales
dummy variables, 156
personal income, 147
seasonal dummy variables, 153
unemployment rate, 150
correlation matrix, 124
market share multiple regression model, 102–103
multiple linear regression, 87–89
Multiple linear regression
approximate 95% confidence interval, 89
dummy variables, 108–111
general form of, 76
point and interval estimate, 89–90
Stoke’s Lodge model
actual vs. predicted regression estimates, 90
explanatory power of the model, 84–87
model does make sense?, 78–80
monthly room occupancy, 78
multicollinearity, 87–89
serial correlation, 87
statistical significance, 80–84
Multiplicative functions, 136–139
Nominal data, 5
Nonlinear regression models
cubic functions, 130–134
multiplicative functions, 136–139
quadratic functions, 128–131
reciprocal functions, 134–136
Ordinal data, 5–6
Ordinary least squares (OLS) regression model
annual values for women’s clothing sales, 28–29
criterion for, 27–28
data analysis in Excel, 32–37
evaluation process
explanatory power of model, 50
model does make sense?, 40–41
serial correlation, 50–53
statistical significance, 41–50
formal
alternative models, 179–181
mathematical approach of, 171–174
R-square development, 174–176
scattergram of Miller’s foods’ market share, 177–179
mathematical assumptions
dispersion, 31
normal distribution, 31–32
probability distribution, 30–31
Stoke’s Lodge occupancy
explanatory power of, 55–56
model makes sense?, 54–55
serial correlation, 55
statistical significance, 56
theory vs. practice, 32
Over specification of regression model. See multicollinearity
Personal income (PI)
Abercrombie & Fitch sales, 143–144
correlation matrix, 153, 156
scattergram, 14–16
Point estimate
college basketball winning percentage, 69
definition of, 66
illustration of, 66
market share multiple regression model, 103–104
multiple linear regression, 89–90
women’s clothing sales, 68
Population, 183–184
Population parameter, 184
Power function. See Multiplicative functions
Probability distribution
ordinary least squares (OLS) regression model, 30–31
p-value, 82–84
Quadratic functions, 128–131
Range, 186
Ratio data, 7
Reciprocal functions, 134–136
Regression analysis
Abercrombie & Fitch sales regression model
dummy variables (RUEHL, Gilly Hicks), 145, 153–157
personal income, 143–147
seasonal dummy variables, 144, 150–153
unemployment rate, 144, 147–150
in business applications
cross-sectional data, 2–3
time-series data, 3–4
college basketball winning percentage
actual vs. predicted values, 20
cross-sectional data, 18, 19
scatterplot, 19
data types
interval data, 6–7
nominal data, 5
ordinal data, 5–6
ratio data, 7
description of, 11
nonlinear regression models
cubic functions, 130–134
multiplicative functions, 136–139
quadratic functions, 128–131
reciprocal functions, 134–136
predicted warnings, 20–21
women’s clothing sales
actual vs. predicted results, 16–17
vs. personal income, 14–16
scattergram, 14–16
time-series data, 14
R-Square. See Coefficient of determination
RUEHL, dummy variable
Abercrombie & Fitch sales, 153–157
correlation matrix, 156
hypothesis, 145
Sample, 183–184
SC. See Schwarz criterion
Scattergram
cubic functions, 128–132
Miller’s foods’ market share
advertising, 179
index of competitor’s advertising, 178
price, 178
OLS regression models, 42, 43
reciprocal functions, 135
women’s clothing sales, 14–16
Schwarz criterion (SC), 177
Seasonal dummy variables
Abercrombie & Fitch sales regression model
explanatory power of model, 152
hypothesis, 144
multicollinearity, 153
serial correlation, 152–153
statistical significance, 152
correlation matrix, 153, 156
womens’ clothing sales (WCS)
complete regression results, 114
monthly basis, 111, 112
multiple regression model, 112–113
regression analyses, 115
regression coefficients, 114–115
UMICS and WUR, 115–117
Second reciprocal function, 136
SEE. See Standard error of the estimate
Serial correlation
Abercrombie & Fitch sales
dummy variables, 156
personal income, 147
seasonal dummy variables, 152–153
unemployment rate, 150
causes of, 52
market share multiple regression model, 102
multiple linear regression, 87
ordinary least squares (OLS) regression model, 50–53
Stoke’s Lodge model, 56
Simple linear regression marker share model, 96–97
Slope
basketball winning percentage, 26–27
definition of, 25
women’s clothing sales model, 25–26
Software programs
Akaike information criterion, 177
Schwarz criterion, 177
SSR. See Sum of squared regression
Standard deviation, 186
Standard error, 187
Standard error of the estimate (SEE), 66–67
approximate 95 percent confidence interval, 66–67
Excel’s regression output, 69–70
market share model, 103
Statistical significance
Abercrombie & Fitch sales
dummy variables, 154–155
personal income, 145
seasonal dummy variables, 152
unemployment rate, 148
market share multiple regression model, 99–101
multiple linear regression, 80–84
ordinary least squares (OLS) regression model, 41–50
Stoke’s Lodge occupancy, 55
Stoke’s Lodge occupancy
monthly room occupancy, 118
multiple linear regression
actual vs. predicted regression estimates, 90
explanatory power of the model, 84–87
model does make sense?, 78–80
monthly room occupancy, 78
multicollinearity, 87–89
serial correlation, 87
statistical significance, 80–84
ordinary least squares (OLS) regression model
explanatory power of, 55–56
model makes sense?, 54–55
serial correlation, 56
statistical significance, 55
regression results, 123
Sum of squared regression (SSR), 86
t-distribution, 59
Time-series data, 3–4
Total variation, 175
t-ratio, 46, 49, 55
t-test, 42, 45, 46. See also hypothesis test
UMICS. See University of Michigan Index of Consumer Sentiment
Unemployment rate, 144, 147–150, 153, 156, 163
Unexplained variation, 175
University of Michigan Index of Consumer Sentiment (UMICS), 115–116
Variance, 186–187
Women’s clothing sales (WCS)
actual vs. predicted results, 16–17
annual values for OLS model, 28–29
approximate 95% confidence interval estimate, 70–72
dummy variables
complete regression results, 114
monthly basis, 111, 112
multiple regression model, 112–113
regression analyses, 115
regression coefficients, 114–115
UMICS and WUR, 115–117
intercept for, 25–26
partial regression statistics, 72
vs. personal income, 14–16
point estimate, 68
scattergram, 14–16
slope for, 25–26
time-series data, 14
Women’s unemployment rate (WUR), 116, 117