Multivariate Models Regression Models A Model A statement

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 Adjusted squared multiple R: 0. 516 Effect CONSTANT NEWSIZE Regression Residual Standard error of estimate: 20. 419 Coefficient Std Error -8. 667 25. 381 2. 012 1. 138 Analysis of Variance Source Sum-of-Squares 207571. 306 193878. 246 Squared multiple R: 0. 517 Std Coef Tolerance 0. 000 0. 719 . 1. 000 t P(2 Tail) -4. 307 22. 312 df Mean-Square F-ratio P 1 465 207571. 306 416. 942 497. 842 0. 000

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 + b 1(Building Size) + b 2(Families)

Further extension of Model of Determinants of Housing Value Dep Var: NEWVAL N: 467 Multiple R: 0. 724 Adjusted squared multiple R: 0. 522 Effect CONSTANT NEWSIZE FAMILIES Regression Residual Standard error of estimate: 20. 284 Coefficient Std Error -2. 551 25. 893 -5. 626 3. 029 1. 146 2. 094 Analysis of Variance Source Sum-of-Squares 210541. 070 190908. 482 Squared multiple R: 0. 524 Std Coef Tolerance 0. 000 0. 734 -0. 087 . 0. 972 t P(2 Tail) -0. 842 22. 595 -2. 687 df Mean-Square F-ratio P 2 464 105270. 535 411. 441 255. 858 0. 000 0. 400 0. 007

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 (V 72) • Household Income: Annual household income from all sources (V 38) • Food Costs = a + b(Household Income)

The Relationship between Household Food Costs and Family Income REGRESS MODEL V 72 = CONSTANT+V 38 Dep Var: V 72 N: 638 Multiple R: 0. 632 Adjusted squared multiple R: 0. 399 Effect CONSTANT V 38 Regression Residual Standard error of estimate: 69. 890 Coefficient Std Error 140. 187 0. 192 6. 896 0. 009 Analysis of Variance Source Sum-of-Squares 2070301. 432 3106609. 876 Squared multiple R: 0. 400 Std Coef Tolerance 0. 000 0. 632 . 1. 000 t P(2 Tail) 20. 328 20. 587 df Mean-Square F-ratio P 1 636 2070301. 432 4884. 607 423. 842 0. 000

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 (V 12) • Food Costs = a+ b 1(Household income) + b 2(Family size)

Modelling the Determinants of Food Costs REGRESS MODEL V 72 = CONSTANT+V 38+V 12 Dep Var: V 72 N: 638 Multiple R: 0. 715 Adjusted squared multiple R: 0. 509 Effect CONSTANT V 38 V 12 Standard error of estimate: 63. 146 Coefficient Std Error 86. 819 0. 159 15. 606 7. 654 0. 009 1. 300 Analysis of Variance Source Sum-of-Squares Regression 2644914. 245 Residual 2531997. 063 Squared multiple R: 0. 511 df 2 635 Std Coef Tolerance 0. 000 0. 523 0. 351 Mean-Square 1322457. 123 3987. 397 . 0. 902 F-ratio 331. 659 t P(2 Tail) 11. 343 17. 883 12. 004 P 0. 000

Visualizing Multiple Regression