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

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)

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

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)

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

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)

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

The Relationship of Food Costs and Household Income

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)

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

Visualizing Multiple Regression