A
Adjusted R squared, 34
Adjusted R2, 67
Alternative hypotheses, 64, 78
Analysis of variance (ANOVA), 18, 34, 61
Analysis ToolPak, 27
Autocorrelation, 128
Average consumption, 13
Average error or regression, 26, 34, 35, 120
Average income, 14
B
Backward elimination, 54
Best linear unbiased estimators (BLUEs), 123
Beta-hat-sub-one, 10
Bonferroni correction, 93
Breusch–Godfrey test, 128
Breusch–Pagan test, 127
Bureau of Economic Analysis,
36, 72
C
Causality
association, 86
ceteris paribus, 87–88
direction of causality, 85
role of theory, 84
Ceteris Paribus, 47, 87–88
Chi-square distribution function, 60
Coefficients in regression analysis, 4
Coefficients or slopes, 4
Coefficient of determination, 34, 35, 46, 66–67, 80
Coefficients of simple regression, 71–74
Coefficients, 42–43
Common mistakes, 52, 78
Conditional expected value, 43, 118
Constant error variance, 126
Consumption function, 71–74
Consumption model’s coefficients, 11, 74–77
Consumption, 36, 71
Control variables, 88
Controlling practice, 47
Correlation coefficient (ρ), 68
Cross-sectional analysis, 108
D
Degrees of freedom (df), 18, 35, 93
Demand
curve, 44
schedule, 87
theory, 84
De-trended data, 108
Diminishing marginal productivity, law of, 112−115
Dummies, too many, 91
Dummy variable, 90, 91, 93, 96, 98
Dummy variables
advantages, 92
creating, 94–99
Durbin–Watson test, 128
E
Economic theory, 44, 47, 54, 59, 71, 72
Elasticity, 5
Endogenous variable, 50, 119
Engel curve, 88
Error, 21, 24−26
Error term or ε, 8, 9, 117, 120
Errors in measurement, 24, 120
Estimated parameters, 12
Estimating Y, 50–52
Estimators, 121
Excel, in multiple regression, 55–58
Exogenous variable, 42, 53
Expected outcome, 42
Expected value, 15, 25
Explained variance, 61
F
F distribution, 68
F test completion, 65–66
Feasible generalized least square (FGLS), 128
G
Gauss–Markov theorem, 124
General model, 41
Goodness of fit, 46, 50, 59, 72, 101
adjusted R2, 67
coefficient of determination or R2, 66–67
F statistics, 60–64
F test completion, 65–66
R2 and F, relation, 68–69
R2 and SSR, difference
between, 67
R2 and ρ, relation, 68
testing, 59
two or more independent variables, 64–65
Growth domestic product (GDP), 114
H
Heteroscedasticity, 126
Homoscedasticity, 126
I
Income–consumption curve, 88
Independent or exogenous variable, 41
Individual error, 15, 23, 25
Inferential statistics, 59
Inferior good, 84
Intercept, 77
K
Kolmogorov–Smirnov test, 125
L
Least squared errors, 22
Least squares, method of
output, 18−22
regression procedure, 13−18
squared (individual) errors, minimize, 22−26
M
Marginal product, 112
Marginal propensity to consume (MPC), 1, 2, 72, 77
Mathematical functions, 7
Mean consumption (µC), 18
Mean of errors, 42
Mean of squared error (MSE), 24, 35, 60, 61, 120
Mean square regression (MSR), 21, 60, 61
Mean square residual, 21
Mean squared (MS) values, 19, 34
Measurement scales, 89
Method of least squares, 11, 15
Minitab software, 53
Misspecification, 53–55
Model, 3
MS regression, 40
MS residual, 40
Multicollinearity, 53, 54
Multiple regression, 42
coefficients, 42–43
common mistakes, 52
estimating Y, 50–52
example, 43–50
general model, 41
misspecification, 53–55
multiple regression in excel, 55–58
N
Negative income elasticity, 84
Nonlinear statistical analysis, 111
Non-negative consumption, 78
Normality, 125
Null hypothesis, 46, 47, 59, 63, 65, 66, 76, 77, 78, 79, 103
O
Observations, 34
Omitted variable bias, 53
One independent variable, 12, 62–64
Ordinary least squares (OLS), 13
Output, 18−22
P
Parameters, 4
Perfect multicollinearity, 92
Point estimate, 121
Price elasticity, 5, 6
Production function, 111
Q
Qualitative data, 89
Qualitative independent variables, 90
Qualitative variables in regression
creating dummy variables, 94–99
dummy variables, advantages, 92
interpretation of, 93
qualitative data, 89
qualitative independent variables, 90
too many dummies, 91
Quantity demanded, 5
R
R2 and F, relation, 68–69
R2 and SSR, difference between, 67
R2 and ρ, relation, 68
R2. See Coefficient of Determination
Random component, 8
Random error, 8
Random numbers, generate, 31
Rates of change, 113
Real data example, 36–40
Regression, 22, 27−30, 34
Regression analysis, pitfalls, 50, 55
cross-sectional data, multicollinearity in, 108
forming incorrect hypotheses, 101−105
independent variables, 109−110
linearity, 111
multicollinearity, 105−108
Regression assumptions, 124
constant error variance, 126
estimators, 121
heteroscedasticity, 126
need, 117
normality, 125
regression assumptions, 124
serial correlation, 127
Regression coefficients
coefficient of determination, 80
coefficients of simple regression, 71–74
common mistakes, 78
consumption model’s coefficients, 74–77
test of hypothesis, 77–78
Regression concept
regression model, mathematical equation to, 7–9
regression, meaning of, 9−12
variables, relationship between, 1–7
Regression line, 22, 23
Regression model, 2, 7, 8, 25, 36
Regression model, mathematical equation to, 7–9
Regression of consumption on income, 39
Regression output, 21
Regression procedure, 13−18
Regression sum of squares, 20
Regression, meaning of, 9−12
Regression, output and its, 32−36
Residual sum of squares, 18, 21
Role of theory, 84
S
Sample variance, 19
Scatter plot, 13, 14
Seed value, 31
Serial correlation, 85, 127
Shapiro–Wilk test, 125
Significance F, 47
Simple linear regression, excel
example, 30
generate random numbers, 31
real data example, 36–40
regression, 27−30
regression, output and its, 32−36
Skew and Kurt functions, 125
Slope parameter (β), 6
Smaller variance, 22, 23
Smallest average error, 21
Spurious correlation, 108
Spurious regression, 55
Square of deviation of consumption, 18
Squared (individual) errors, minimize, 22−26
Standard deviation, 120
Standard error, 34, 35, 49
Statistic, 4
Stepwise regression, 54
Subscript K, 41
Sum of all individual errors, 22
Sum of squared deviations of consumption from mean of consumption, 18
Sum of squared errors (SSE), 21, 26
Sum of squared regression, 26
Sum of squared residual, 26
Sum of squares due to regression (SSR), 67
sum of squares of residual, 18
Sum of squares regression, 20
Sum of squares total (SST), 18, 19, 62
T
t statistics, 63, 65, 72, 76, 79
Test of hypothesis, 77–78
Three dots, 41
Time series analysis, 108
Tolerance level, 109
Total sum of squares, 18, 19
Two or more independent variables, 64–65
Two parameters, 12
Type I error, 46, 59, 81, 93
Type II error, 81, 108, 126
Type III error, 80, 107
U
Unexplained variance, 61
Unrelated regression analyses, 93
V
Validity, 24, 120
Variables, relationship between, 1–7
Variance inflation factor (VIF), 109
Variance of regression model, 35
Variance, 26, 61
W
White test, 127
Z
Zero slope, 63