QM Project Statistical Analysis of Rent Paid by U.S.

Households

Group Mentor :Prof. Manish Thakkar

Group Members:Riddhima Kartik (20151037)Rishabh Surana (20151038)

Objective :

To find the extent of relation/dependency of variables(dependent and independent) by using various statistical tools like Correlation, Regression and Independence test using SPSS.

Variables Involved

Dependent Variables : RentIndependent Variables : Household Income Electricity Cost Gas Cost Rooms Per House Vehicle Per Household

Software Used : SPSS (Statistical Package for the Social Sciences)

Statistical Methods Used :

Normality Test Correlation with Scatter plot. Multiple Regression Analysis

Condition to Apply Parametric Statistical Methods-

Parametric statistical methods(ANOVA and Linear Regression etc.) requires that dependent must be normally distributed.

To check Normality by SPSS: Steps Involved : Analysis->Descriptive->Explore->Plot-

>Normality plot-> ok

Operations Involved

Test of Normality

Considering: 1. No. of Person 2. No. of Vehicles 3. No. of Rooms

Normality Test w.r.t. No. of Persons

Normality Test w.r.t. No. of Rooms

Normality Test w.r.t. No. of Vehicles

Correlation Test : Hypothesis considered: Hypothesis 1 H0 : There is no significant correlation between Rent and Household Income. Ha : There is significant correlation between Rent and Household Income.Hypothesis 2 H0 : There is no significant correlation between Rent and Electricity Cost. Ha : There is significant correlation between Rent and Electricity Cost.Hypothesis 3 H0 : There is no significant correlation between Rent and Gas Cost. Ha : There is significant correlation between Rent and Gas Cost.

Correlation between: Rent and Household Income = .000Rent and Electricity Cost = .009 Rent and Gas Cost = .013

Therefore, we reject all three nullHypothesis and can say that thesefactors have significant impactover rent

Confidence Level taken is 95%

To check Strength of Correlation we can see Scatter plot ->

Graphical analysis : Scatter Plot (Household Income)

Graphical analysis : Scatter Plot (Electricity Cost)

Graphical analysis : Scatter Plot (Gas Cost)

Strength with Household Income: Moderate, not very strong.Strength with Electricity Cost: WeakStrength with Gas Cost: Weak

Steps Involved :-(Graph->chart-builder->drag the simple scatter graph):- If all the scatter points are in same straight line then we have strong relationship between them.

Multiple Regression :Ho : Variation in Y(Dependent variable(Rent)) is unrelated to variation in

X(Independent variable(Household Income, Electricity Cost, Gas Cost)).OrHo: Correlation between X(Household Income, Electricity Cost, Gas Cost) and

Y(Rent) is 0.

Ha: Correlation between X(Household Income, Electricity Cost, Gas Cost) and Y(Rent) is not 0.

Regression Summary

Summary Results

ResultR^2 value is 28.6, which means that 28.6% variation in Rent is due to

Household Income, Electricity Cost, Gas Cost and rest because of other factors.

Constant = 1168.89 -> This much will be the basic Rent that households have to pay irrespective of other factors.

p-value for all the variables are quite lower than our significance level that is 0.05. So, Null hypothesis is rejected and we can conclude that :

Conclusion : Correlation between X(Household Income, Electricity Cost, Gas Cost) and Y(Rent) is not 0.

Y = 1168.89 + .003A + 2.415B + 4.481C

THANK YOU