# Statistics Paper - Condosales

**Topics:**Regression analysis, Linear regression, Statistics

**Pages:**5 (951 words)

**Published:**March 12, 2009

A. Brief introduction to the case

This case involves an investigation of the factors that affect the sale price of oceanside condominium units. The sales data were obtained for a new oceanside condominium complex consisting of two adjacent and connecting eight-floor buildings. The complex contains 200 units of equal size (approximately 500 square feet each).

Variables

• Dependent variable

1. Sale price: Y

• Independent variables

1. Floor height: x1

2. Distance from elevator: x2

3. View of the ocean: x3

4. End unit: x4

5. Furniture: x5

Issues identified

• To build a regression model that accurately predicts the sale price of a condominium unit sold at auction. • Use graphs to demonstrate how each of the independent variables in the model affects price.

B. Case Analysis

1. Creating the deterministic regression model

Since there are five independent variables, there shall be 5 variables in our initial first order regression model:

E(y) = β0 + β1x1 + β2 x2 + β3 x3 + β4 x4 + β5 x5 + (

Using the data in the CD, we find the SPSS printout for the case as below:

Coefficients (a)

|Model | |Unstandardized Coefficients |Standardized |t |Sig. | | | | |Coefficients | | | | | |B |Std. Error |Beta | | | | |B |Std. Error |Beta | |1 |.789(a) |.623 |.604 |21.324 |

a Predictors: (Constant), distview, floorsq, furnish, endunit, distance, floorview, floordist, view, distsq, floor

ANOVA(b)

Model | |Sum of Squares |df |Mean Square |F |Sig. | |1 |Regression |147387.091 |9 |16376.343 |35.614 |.000(a) | | |Residual |91505.684 |199 |459.828 | | | | |Total |238892.775 |208 | | | | |a Predictors: (Constant), distview, floorsq, endunit, distance, floorview, floordist, view, distsq, floor b Dependent Variable: price

H0: β1 = β2 = β3 = β4 …10 = 0

Ha: At least one of the coefficients is non-zero

Test statistic: F = (R2/k)/ {(1-R2)/[n-(k+1)]}

Rejection region: F> F0.01 = 3.02

In this case, n = 209, k = 9, n-(k+1) = 199, α = 0.01

From the SPSS printout, we find that the computed F value is 35.614. Since this value greatly exceeds the tabulate value of 3.02, we conclude that at least one of the model coefficients β1, β2, β3 and β4 is non-zero. Therefore, this global F-test indicates that the first-order model E(y) = β0 + β1x1 + β2 x2 + β3 x3 + β4 x4 + ( is useful for predicting sale price.

2. Hypothesis Testing of Interactive Terms

E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β6x12 + β7x22 + β8x1x2 + β9x1x3 + β10x2x3

i) The hypotheses of interest concern the interaction parameter β8. Specifically,

H0: β8 = 0

Ha: β8 < 0

Test statistic: t = -1.804, p-value = 0.073, respectively.

The lower-tailed p-value, obtained by dividing the two-tailed p-value in half, is 0.073/2 = 0.0365. Since we are testing using α = 0.1, α exceeds the p-value, thus we can reject H0 and conclude that the rate of change of the sale price of the condos with floor height(x1) decreases as the distance(x2) increases; that is x1 and x2 interact positively. Thus, it appears that the interaction term should be included in the model.

ii) The hypotheses of interest concern the interaction parameter β9. Specifically,

H0: β9 = 0

Ha: β9 > 0

Test statistic: t = -4.507, p-value = 0, respectively.

The upper-tailed p-value, obtained by dividing the two-tailed p-value in half, is 0/2 =0. Since we are testing using α = 0.1, α exceeds the p-value, thus we can reject H0 and conclude that the rate of change of the sale price of the condos with floor height(x1) increases as the view of the ocean(x3)...

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