A
Abercrombie & Fitch sales regression model
five-step evaluation model
dummy variables (RUEHL, Gilly Hicks), 152–156
personal income, 143–146
seasonal dummy variables, 148–152
unemployment rate, 146–148
hypothesis
dummy variables (RUEHL, Gilly Hicks), 143
personal income, 141–142
seasonal dummy variables, 142
unemployment rate, 142
Adjusted coefficient of determination, 84
Adjusted R-square, 84
AIC. See Akaike information criterion
Akaike information criterion (AIC), 162–163
Analysis of variance (ANOVA), 86, 172
Annual values for women’s clothing sales (AWCS), 28–30
ANOVA. See Analysis of variance
Approximate 95% confidence interval estimate
college basketball winning percentage, 72–73
concept of, 66–67
market share multiple regression model, 102
multiple linear regression, 88–89
women’s clothing sales (WCS), 70–72
AWCS. See Annual values for women’s clothing sales
B
Bivariate linear regression (BLR) model, 24
Business applications, regression analysis
cross-sectional data, 2–3
time-series data, 3–4
C
Central tendency
mean, 170
median, 171
mode, 171
Cobb-Douglas production function, 135
Coefficient of determination
adjusted, 84
definition of, 50
development of, 160–162
College basketball winning percentage
actual vs. predicted values, 20–21
approximate 95% confidence interval estimate, 72–73
cross-sectional data, 18–19
point estimate, 68–69
scatterplot, 19–20
Computed test statistic, 45, 49, 85
Confidence interval, 66
Constant. See intercept
Correlation matrix
independent variables, 122
Miller’s Foods’ market share regression, 101
multicollinearity, 122
personal income, 152
RUEHL and Gilly Hicks, 155
seasonal dummy variables, 152
unemployment rate, 152
Critical values
Durbin–Watson statistic, 59–60
F-distribution at 95% confidence level, 92–93
F-test, 86
hypothesis test, 45
Cross-sectional data, 2–3
Cubic functions, 129–132
D
Data Analysis
in Excel 2003, 8
in Excel 2007, 8
in Excel 2010, 9
OLS regression model in Excel, 32–38
Data types
interval data, 6–7
nominal data, 5
ordinal data, 5–6
ratio data, 7
Degrees of freedom, 56–57
Dependent variable, 24
Dispersion
range, 171–172
standard deviation, 172
standard error, 173
variance, 172–173
Dummy variables
Abercrombie & Fitch sales regression model
five-step evaluation model, 152–156
hypothesis, 143
definition of, 106
multiple linear regression, 106–108
seasonality, 108–115
uses of, 106
women’s clothing sales, 108–115
Durbin–Watson (DW) statistic, 51–52, 59–63, 101
E
Explained variation, 161–162
Explanatory power of model
Abercrombie & Fitch sales
dummy variables, 154
personal income, 145
seasonal dummy variables, 150–151
unemployment rate, 147–148
market share multiple regression model, 100–101
multiple linear regression, 84–86
ordinary least squares (OLS) regression model, 49–50
Stoke’s Lodge occupancy, 55
F
Formal OLS regression model
alternative models, 164–167
mathematical approach of, 157–160
R-square development, 160–162
scattergram of Miller’s foods’ market share, 163–165
software programs
Akaike information criterion, 162–163
Schwarz criterion, 162–163
F-statistic, 85–86
G
Gilly Hicks, dummy variable
Abercrombie & Fitch sales, 152–155
correlation matrix, 155
hypothesis, 143
H
Homoscedasticity, 31
Hypothesis test, 43–49
I
Independent variable, 24
Intercept
basketball winning percentage, 26–27
definition of, 24
women’s clothing sales model, 25–26
Interval data, 6–7
M
Market share multiple regression model
approximate 95% confidence interval estimate, 102
explanatory power of model, 100–101
model does make sense?, 97–99
multicollinearity, 101–102
point estimate, 102
serial correlation, 101
statistical significance, 99–100
three-dimensional visual representation, 103–104
Mean, 170
Median, 171
Miller’s Foods’ market share. See also market share multiple regression model
alternative models, 165–167
building and evaluating, 163
scattergram
advertising, 165
index of competitor’s advertising, 165
price, 164
Mode, 171
MONEYBALL, 18, 72
Monthly room occupancy (MRO)
actual and predicted values for, 118, 123
function of gas price, 117
multiple linear regression, 77–78
OLS regression models, 53
Stoke’s Lodge, 116
MRO. See monthly room occupancy
Multicollinearity
Abercrombie & Fitch sales
dummy variables, 155
personal income, 145
seasonal dummy variables, 151
unemployment rate, 148
correlation matrix, 122
market share multiple regression model, 101–102
multiple linear regression, 87–88
Multiple linear regression
approximate 95% confidence interval, 88–89
dummy variables, 106–108
general form of, 76
point estimate of, 88–89
Stoke’s Lodge model
explanatory power of the model, 84–86
model does make sense?, 78–79
monthly room occupancy, 77–78
multicollinearity, 87–88
serial correlation, 86–87
statistical significance, 80–84
Multiplicative functions, 135–137
N
Nominal data, 5
Nonlinear regression models
cubic functions, 129–132
multiplicative functions, 135–137
quadratic functions, 126–129
reciprocal functions, 132–134
O
Ordinal data, 5–6
Ordinary least squares (OLS) regression model
annual values for women’s clothing sales, 28–30
criterion for, 27–28
data analysis in Excel, 32–38
evaluation process
explanatory power of model, 49–50
hypothesis test, 43–49
model does make sense?, 40–41
serial correlation, 50–52
statistical significance, 41–43
formal
alternative models, 165–167
mathematical approach, 157–160
R-square development, 160–162
scattergram of Miller’s foods’ market share, 163–165
formal approach, 157–160
mathematical assumptions
dispersion, 31
normal distribution, 31–32
probability distribution, 30–31
Stoke’s Lodge occupancy
explanatory power of, 55
model makes sense?, 54
serial correlation, 55
statistical significance, 54–55
theory vs. practice, 32
Over specification of regression model. See multicollinearity
P
Personal income (PI)
Abercrombie & Fitch sales, 141–146
correlation matrix, 152, 155
scattergram, 14–16, 26
Point estimate
college basketball winning percentage, 68–69
definition of, 65–66
illustration of, 66
market share multiple regression model, 102
multiple linear regression, 88–89
women’s clothing sales, 68
Population, 169–170
Population parameter, 170
Power functions. See multiplicative functions
Probability distribution
ordinary least squares (OLS) regression model, 30–31
p-value, 82–84
Q
Quadratic functions, 126–129
R
Range, 171–172
Ratio data, 7
Reciprocal functions, 132–134
Regression analysis
Abercrombie & Fitch sales
dummy variables (RUEHL, Gilly Hicks), 143, 152–156
personal income, 141–146
seasonal dummy variables, 142, 148–152
unemployment rate, 142, 146–148
in business applications
cross-sectional data, 2–3
time-series data, 3–4
college basketball winning percentage
actual vs. predicted values, 20–21
cross-sectional data, 18–19
scatterplot, 19–20
data types
interval data, 6–7
nominal data, 5
ordinal data, 5–6
ratio data, 7
description of, 11
nonlinear regression models
cubic functions, 129–132
multiplicative functions, 135–137
quadratic functions, 126–129
reciprocal functions, 132–134
predicted warnings, 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, 152–155
correlation matrix, 155
hypothesis, 143
S
Sample, 169–170
SC. See Schwarz criterion
Scattergram
cubic functions, 129–132
Miller’s foods’ market share
advertising, 165
index of competitor’s advertising, 165
price, 164
OLS regression models, 42
quadratic functions, 126–129
reciprocal functions, 132–134
women’s clothing sales, 14–16, 26
Schwarz criterion (SC), 162–163
Seasonal dummy variables, 108–115, 142, 148–153, 155
Second reciprocal function, 134
SEE. See Standard error of the estimate
Serial correlation
Abercrombie & Fitch sales
dummy variables, 152
personal income, 145
seasonal dummy variables, 151
unemployment rate, 148
causes of, 52
market share multiple regression model, 101
multiple linear regression, 86–87
ordinary least squares (OLS) regression model, 50–52
Stoke’s Lodge model, 55
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, 162–163
Schwarz criterion, 162–163
SSR. See Sum of squared regression
Standard deviation, 172
Standard error, 173
Standard error of the estimate (SEE), 66, 85, 102
Statistical significance
Abercrombie & Fitch sales
dummy variables, 154
personal income, 144–145
seasonal dummy variables, 150
unemployment rate, 147
market share multiple regression model, 99–100
multiple linear regression, 80–84
ordinary least squares (OLS) regression model, 41–43
Stoke’s Lodge occupancy, 54–55
Stoke’s Lodge occupancy
monthly room occupancy, 116–118
multiple linear regression
explanatory power of model, 84–86
model does make sense?, 78–79
monthly room occupancy, 77–78
multicollinearity, 87–88
serial correlation, 86–87
statistical significance, 80–84
ordinary least squares (OLS) regression model
explanatory power of, 55
model makes sense?, 54
regression results for, 54
serial correlation, 55
statistical significance, 54–55
Sum of squared regression (SSR), 85
T
t-distribution, 46, 57–58
Time-series data, 3–4
Total variation, 161
t-ratio. See computed test statistic
t-test, 43. See also hypothesis test
U
UMICS. See University of Michigan Index of Consumer Sentiment
Unemployment rate, 142, 146–148, 150, 152–153, 155
Unexplained variation, 161–162
University of Michigan Index of Consumer Sentiment (UMICS), 115
V
Variance, 172–173
W
Women’s clothing sales (WCS)
actual vs. predicted results, 16–17
annual values for OLS model,28–30
approximate 95% confidence interval estimate, 70–72
dummy variables, 108–115
intercept for, 25–26
vs. personal income, 14–16
point estimate, 68
scattergram, 14–16
slope for, 25–26
time-series data, 14