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: Multiple R: Squared multiple R: 0.517
Adjusted squared multiple R: Standard error of estimate:
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT
NEWSIZE
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression
Residual

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: Multiple R: Squared multiple R: 0.524
Adjusted squared multiple R: Standard error of estimate:
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT
NEWSIZE
FAMILIES
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression
Residual

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: Multiple R: Squared multiple R: 0.400
Adjusted squared multiple R: Standard error of estimate:
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT V
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression
Residual

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: Multiple R: Squared multiple R: 0.511
Adjusted squared multiple R: Standard error of estimate:
Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail)
CONSTANT V V
Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P
Regression
Residual

12. Visualizing Multiple Regression