Quantitative Techniques in Anaylsis

SPSS OUTPUT MISSING VALUES FORMULAS

Introduction to Linear Regression

1. Straight line
2. Difference between y and y hat
3. Beta and Constant
4. Residual or Error
5. Difference between Simple Linear Regression and Multiple Linear Regression
6. Sample Size in Linear Regression. Note: the expected R for random data is k/(N − 1)

Assumption of Multiple Linear Regression

• Normality    
• Homoscedasticity
• Independent error  ( No auto correlation for different point in time or Spatial autocorrelation for different spatial locations)
• Endogeneity
• Specification Error ( omitted variable bias, Irrelevant variable included Measurement Error, simultaneity bias)
• Lack of multicollinearity
• Consistent Coefficient

Assumption Testing

• Normality    (Kolmogorov-Smirnov Test and the Shapiro-Wilk Test. 2. Lilliefors test, 3. Jarque–Bera test)
• Homoscedasticity ( 1 White Test 2 Breusch–Pagan test  )
• Independent error ( Durbin Watson 2. Breusch–Godfrey serial correlation LM test)
• Endogeneity (Durbin-Wu-Hausman Test)
• Specification Error (Ramsey RESET test)
• Lack of multicollinearity ( Tolerance and Variance Inflation Factor (VIF)
• Consistent Coefficient (Chow Test for structural break used in time series)

Regression Methods

• Enter
• Stepwise ( Backward)

Formulas

• R
• R2
• Adjusted R2
• Standard error of estimate
• SSR
• SSE
• SST
• Dfr
• Dfe
• Dft
• MSR
• MSE
• F
• t
• y hat

Interpretation

Model Summary: Assessing the Goodness of fit: R and R square

ANOVA Table: F Value

Coefficient Table: Assessing the individual predictors

Notation

Y = Dependent Variable.

X = Independent Variable

 Ŷ = Predicted Y

SS = Sum of Square

MS = Mean Square

Df = Degree of Freedom

Regression = R

Residual = E

Total = T

N = Sample Size

Formulas

SS.T = SS.R + SS.E

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