STATISTICS FOR MANAGERS

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1. Multiple regression model

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2. Methodology

• Least squares method - minimize sum of squared differences of the actual values from the estimated values

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• Excel and pH Stat (housing data)

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3. Interpretation

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Ex. - 

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4. Dummy variables

• Takes on a value of 1 (if criteria met) or 0 (otherwise)

• Allow categorical data to be represented

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a. Interpretation

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b. Multiple options

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5.  Prediction

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6. Measures of variation

a. Sum of squares

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(1) Total sum of squares (SST)

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(2) Regression sum of squares (SSR)

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(3) Error sum of squares (SSE)

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7. Evaluating the overall model

a. Coefficient of multiple determination

• Proportion of the variation in variable Y explained by the multiple regression model involving the independent variables X₁, X₂, . . . X_K

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• Morningstar

• The Vanguard Group

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b. Adjusted r-square

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c. F-test

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8. Inferences about coefficients

a. Hypothesis tests

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b. Confidence intervals

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9. Assumptions and problems

• Use residual analysis to evaluate violation of assumptions

a. Normality of errors

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b. Homoscedasticity

• Error terms have a constant variance for all values of X

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• Heteroscedasticity - violation of assumption of constant variance of error terms

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(1)  Problems

• Least-squares estimator is inefficient => standard error larger than otherwise => less likely to reject null hypothesis that the independent variable coefficient = 0

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(2)  Evaluation

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(3)  Dealing with heteroscedasticity

• Use weighted least-squares

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c. Independence of errors

• Errors are unrelated

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• Autocorrelation - violation of assumption of independence of error terms

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(1)  Problems

• True variance of estimated coefficient is higher, but estimated variance is lower => more likely to reject null hypothesis

• Model appears better than it actually is (R² impacted too)

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(2)  Evaluation

• Use Durbin-Watson statistic

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(3)  Dealing with autocorrelation

• Use two-stage least-squares

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d. Multicollinearity

• Explanatory variables highly correlated

Ex. - 

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(1)  Problems

• Difficult to interpret coefficients of independent variables

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(2)  Evaluation

• Use variance inflationary factor (VIF)

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(3)  Dealing with multicollinearity

• Could drop some of the variables that are correlated

• Problematic if theory says variables should be in model

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10.  Logistic regression

• Use categorical variable as the dependent variable

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a.  Methodology

• Use maximum likelihood estimation

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b.  Interpretation

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11. Ethical considerations

Problems if:

a. Variables intentionally omitted

b. Observations deleted without explanation

c. Assumptions not evaluated