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Multivariate Models

Multivariate Models. Regression. Models. A Model: A statement of the relationship between a phenomenon to be explained and the factors, or variables, which explain it. Steps in the Process of Quantitative Analysis: Specification of the model Estimation of the model Evaluation of the model.

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Multivariate Models

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  1. Multivariate Models Regression

  2. Models • A Model: A statement of the relationship between a phenomenon to be explained and the factors, or variables, which explain it. • Steps in the Process of Quantitative Analysis: • Specification of the model • Estimation of the model • Evaluation of the model

  3. Model of Housing Values and Building Size • There is a linear relationship between building size and housing value. • As the size of the building increases, the value of the house increases. • Building Size = Square Feet/1000 • Housing Value = 1905 Property Assessment in 2002 dollars/1000 • Housing Value = a + b(Building Size)

  4. Model of Housing Values and Building Size Dep Var: NEWVAL N: 467 Multiple R: 0.719 Squared multiple R: 0.517 Adjusted squared multiple R: 0.516 Standard error of estimate: 20.419 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT -8.667 2.012 0.000 . -4.307 0.000 NEWSIZE 25.381 1.138 0.719 1.000 22.312 0.000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 207571.306 1 207571.306 497.842 0.000 Residual 193878.246 465 416.942

  5. Extending the Model… • Housing Value is determined by building size and the number of families in the dwelling. • Families = no. of families in the dwelling • Housing Value = a + b1(Building Size) + b2(Families)

  6. Further extension of Model of Determinants of Housing Value Dep Var: NEWVAL N: 467 Multiple R: 0.724 Squared multiple R: 0.524 Adjusted squared multiple R: 0.522 Standard error of estimate: 20.284 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT -2.551 3.029 0.000 . -0.842 0.400 NEWSIZE 25.893 1.146 0.734 0.972 22.595 0.000 FAMILIES -5.626 2.094 -0.087 0.972 -2.687 0.007 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 210541.070 2 105270.535 255.858 0.000 Residual 190908.482 464 411.441

  7. Model of Household Food Costs and Household Income • There is a linear relationship between food costs and household income. • As household income increases, the household’s expenditure on food increases. • Food Costs: Total spent by the family per year on food (V72) • Household Income: Annual household income from all sources (V38) • Food Costs = a + b(Household Income)

  8. The Relationship between Household Food Costs and Family Income REGRESS MODEL V72 = CONSTANT+V38 Dep Var: V72 N: 638 Multiple R: 0.632 Squared multiple R: 0.400 Adjusted squared multiple R: 0.399 Standard error of estimate: 69.890 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT 140.187 6.896 0.000 . 20.328 0.000 V38 0.192 0.009 0.632 1.000 20.587 0.000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 2070301.432 1 2070301.432 423.842 0.000 Residual 3106609.876 636 4884.607

  9. The Relationship of Food Costs and Household Income

  10. Extending the Model… • Food Costs are determined by household income and by the number of people in the household. • Family Size = no. of people in the household (V12) • Food Costs = a+ b1(Household income) + b2(Family size)

  11. Modelling the Determinants of Food Costs REGRESS MODEL V72 = CONSTANT+V38+V12 Dep Var: V72 N: 638 Multiple R: 0.715 Squared multiple R: 0.511 Adjusted squared multiple R: 0.509 Standard error of estimate: 63.146 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT 86.819 7.654 0.000 . 11.343 0.000 V38 0.159 0.009 0.523 0.902 17.883 0.000 V12 15.606 1.300 0.351 0.902 12.004 0.000 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 2644914.245 2 1322457.123 331.659 0.000 Residual 2531997.063 635 3987.397

  12. Visualizing Multiple Regression

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