SAS slide sdfdsfdsfsd dfsdsdfwyr6u

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Group members:

AINIL AFIQAH BT. MOHD HAMDANAUWATIF BT. U-UDEEB MAHFOUZ JAZOULY

NUR HAYATUL NISAB BT. MAT SARIP

Prepared for :

MR. MOHD NOOR AZAM B. NAFI

Group :

D2 CS221 5A

Introduction :

STA 610SAS Programming

• Source of Dataset : Journal of Statistics Education - Data Archive. (http://www.amstat.org/publications/jse/jse_data_archive.htm)

• This data set contains information for individual residential properties sold in Ames, Iowa from 2006 to 2010.

• Description of Dataset : See table

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Result &

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https://www.google.com.my/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CCgQFjAA&url=http://www.amstat.org/publications/jse/jse_data_archive.htm&ei=J-unUv2zH8K5iQeB6oHYCw&usg=AFQjCNEYXvYKh6wGOpt5oZmIv4kBqu0eXg

http://www.amstat.org/publications/jse/jse_data_archive.htm

Introduction :


In order to conduct this project, we have set several

objectives:

a) To check model adequacy: normality, homogeneity

of variance and independency assumption.

b) To check the significance level of the model.

c) To identify if there is relationship between

dependent variable and independent variable.

Objectives :

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Introduction :


In order to conduct this project, we have set several

objectives:

a) To check the existence of multicolinearity.

b) To find the best model.

c) To compare Group means and the overall mean

d) To study the correlation between the variable and Sales Price.

Objectives :

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Methodology :

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I. ONE-WAY ANOVA

II. ONE SAMPLE T-TEST

III. TWO INDEPENDENT SAMPLE

IV. LINEAR REGRESSION

V. PIE AND BAR CHART

VI. CORRELATION COEFFICIENT

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Descriptive Statistics :

• Residential Low Density(1) $6,161,600

• Floating Village Residential(2)$3,360,710

• Residential Medium Density(3), Commercial (4), Residential High Density(0)$3,675,339, $ 1,327,476 and $1,189,400

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• Single-family Detached (0):

• 62.72%

Townhouse

Inside Unit :

(2) 1.83%

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• Single-family Detached (0):

• 62.72%

Townhouse

Inside Unit :

(2) 1.83%

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Inferential Statistics :

• to study the effect of Zoning, LotArea, FirstFloor, SecondFloor, GarageArea, LivArea, KitQual, BldgType variables on the SalesPrice.

• CORR procedure is required : computed Pearson correlation

• See output

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• REG procedure : relationship between the variables

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• REG procedure : able to check the multicollinearity in the model .

• See ouput

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• REG procedure : to check the model adequacy.

Normality Assumption :

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Homogeneity Assumption :

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Independence Assumption :

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• REG procedure : used to select the best predictor variable to be included in the model.

• main approach is on the Backward Selection

Final model : ( Best parameter )

Regression Model is significant. See hypothesis

Coefficient of Multiple Determination,𝑅2 = 0.8396

Model Adequacy is checked again.

𝑦= −13172 + 2.17109𝑥2 + 55.71420𝑥3 + 30.91042𝑥5

+ 39.99168𝑥6 + 40049𝑥11 + 55296𝑥12 + 18631𝑥13

+ 26700𝑥71 − 21846𝑥80 − 34193𝑥81

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backward elimination.docx

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• ANOVA procedure : used to perform analysis of variance for these data.

From the output given :

Hypothesis:

𝐻0 ∶ The regression model is not significant

𝐻1 ∶The regression model is a significant

Test Statistic : p-value= <0.0001.

Decision : Since the p-value (<0.0001) < α = 0.05,reject𝐻0.

Conclusion : The regression model is significant

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The ANOVA procedure.docx

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• t - TEST procedure : used to study the means of sales price between the zonings.

• The two – sample t test : compared the mean of sample from Floating Village Residential(2)minus the sample from Commercial(4) –See other comparison

From the output given:

Hypothesis :𝐻𝑜 ∶ 𝜇2 = 𝜇4 , 𝐻𝑜 ∶ 𝜇2 ≠ 𝜇4

(∝ = 0.05)Test statistic :𝒕 ∗ = 9.10Decision rule : 𝑡0.025,28.443 = 2.04667 .Since

𝑡 ∗ = 9.26 > 𝑡0.025,28.443 = 2.04667 , reject𝐻𝑜.

Conclusion :mean of sales price of Floating Village Residential(2) and Commercial(4) are significantly different.

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• t - TEST procedure : used to study the overall mean given by the zonings – One Sampled t – Test

From the output given :

Hypothesis :𝐻𝑜: 𝜇 = $200,000 , 𝐻𝑜: 𝜇 ≠ $200,000(∝ = 0.05)

Test statistic :𝑝 − 𝑣𝑎𝑙𝑢𝑒 = < .0001

Decision rule : 𝑡0.025,228 = 2.05169 (Interpolation)

Since 𝑝 − 𝑣𝑎𝑙𝑢𝑒 = < .0001 < ∝ = 0.05, reject𝐻𝑜.

Conclusion : Mean of sales price is significantly different from $200,000.

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• Since the data is normally distributed, the

parametric test are proceeded.

• Model adequacy checking assumptions are all

satisfied.

• There are several factors that significantly affect

the sale price.

• The best model is : 𝑦 = −13172 + 2.17109𝑥2 +

55.71420𝑥3 + 30.91042𝑥5 + 39.99168𝑥6 +

40049𝑥11 + 55296𝑥12 + 18631𝑥13 +

26700𝑥71 − 21846𝑥80 − 34193𝑥81

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Reference :

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• Buchecker, M., Calhoun, S. and Repole, W. (2004).

SAS Programming I: Essentials. USA: SAS Institute

Inc.

• Kutner, M. H.,Nachtsheim, C. J., Neter, J. and Li, W.

(2005). Applied Linear Statistical Models. New

York: McGraw Hill.

• Daniel W. W. (1990). Applied Nonparametric

Statistics. USA: Brooks/Cole Cengage Learning.

The End

Question & Answer

Output

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Variable Description Unit

X1=ZoningThe general zoning classification of the

sale.0 Residential High Density

1 Residential Low Density

2 Floating Village Residential

3 Residential Medium Density

4 Commercial

X2=LotArea Lot size Square feet (sqft)

X3=FirstFloor Area of First Floor Square feet (sqft)

X4=SecondFloor Area of Second Floor Square feet (sqft)

X5=GarageArea Area of garage Square feet (sqft)

X6=LivArea Size of living area Square feet (sqft)

X7=KitQual Kitchen quality 0 Excellent

1 Good

2 Typical/Average

X8=BldgType Type of building 0 Single-family Detached

1 Townhouse End Unit

2 Townhouse Inside Unit

3 Duplex

4 Two-family Conversion

Y=SalePrice Selling price Dollar ($)

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• Hypothesis :𝐻0 ∶ 𝛽𝑗 = 0, 𝐻1 : 𝛽𝑗 ≠ 0

for at least one j

• Test Statistic :p-value = <0.0001.

• Decision :Since the p-value (<0.0001) < α = 0.05 , reject𝐻0.

• Conclusion :The regression model is significant.

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Normality Assumption :

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Homogeneity Assumption :

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Independence Assumption :

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The SAS System

The TTEST Procedure

Variable: SalePrice (SalePrice)

Zoning Method Mean 95% CL Mean Std Dev 95% CL StdDev

2 197689 174778 220600 44560.9 33187.6 67818.6

4 78086.8 62254.6 93919.0 30792.8 22933.5 46864.4

Diff (1-2) Pooled 119602 92842.8 146361 38300.6 30800.9 50659.9

Diff (1-2) Satterthwaite 119602 92711.0 146493

Method Variances DF t Value Pr > |t|

Pooled Equal 32 9.10 <.0001

Satterthwaite Unequal 28.443 9.10 <.0001

Cochran Unequal 16 9.10 <.0001

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Zoning t- value dft – tabulated

∝𝟐 = 𝟎. 𝟎𝟐𝟓

Decision Conclusion

0 and 1 -4.44 17.86 -2.10226Failed to

reject

𝐻𝑜

There are no

significant

differences

0 and 2 -4.95 21.99 -2.07406

0 and 3 0.03 15.642 2.12394

0 and 4 2.95 16.359 2.11641

Reject

𝐻𝑜

There are

significant

differences

1 and 2 -1.24 32.656 -2.03642

1 and 3 6.06 62.535 1.99916

1 and 4 9.56 44.307 2.01648

2 and 3 6.20 28.793 2.04562

2 and 4 9.10 28.443 2.04667

3 and 4 4.01 39.196 2.02269

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One - Mean Comparison of Sale Price Given BY Zoning

The TTEST Procedure

Variable: SalePrice (SalePrice)

Frequency: Zoning Zoning

N Mean Std Dev Std Err Minimum Maximum

229 127594 57758.0 3816.8 12789.0 289000

Mean 95% CL Mean Std Dev 95% CL StdDev

127594 120073 135114 57758.0 52908.2 63594.2

DF t Value Pr > |t|

228 -18.97 <.0001

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SAS slide sdfdsfdsfsd dfsdsdfwyr6u