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HI6007 Assignment on Statistics and Research Method for Business

Added on - 07 Apr 2020

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Running Head: HI6007 GROUP ASSİGNMENTStudent Name:Partner(s) Name:Course:Professor Name:Date Submitted:HI6007 Group Assignment
HI6007 Group AssignmentTask 11.Descriptive Statistics summary for the sampled data of 50 credit card users:Income($1000s)HouseholdSizeAmountCharged ($)Mean43.483.423963.86Standard Error2.0580.246132.023Median4234090Mode5423890Standard Deviation14.551.74933.55Sample Variance211.723.02871508.74Kurtosis-1.25-0.72-0.74Skewness0.010.53-0.13Range4663814Minimum2111864Maximum6775678Sum2174171198193Count505050Confidence Level (95.0%)4.140.50265.31CommentsThe average household size was computed to be 3.42. The data values arelikely to deviate by 1.739 around this mean value. Further, as read from themedian value, about 50% of the sampled customers had a household size of 3or more. The minimum & maximum household sizes are 1 and 7, respectively.The mean annual Income of sampled customers is $43,480. The data values arelikely to deviate within $14,550 around this mean value. Moreover, about 50%of the customers have an annual income of $42,000 or above, while theremaining 50% below this. The maximum and minimum recorded annualincomes for the sampled data are $21,000 and $67,000, respectively.The average annual amount charged to the credit card holders is $3963.8. Thedata values are likely to deviate by $933.55 around this mean value. Further,the median value suggests that about 50% of the credit card holders werecharged $4,090 or over while the remaining 50% below this. The minimumPage |1
HI6007 Group Assignmentand maximum amounts charged to credit card holders are $1,864 and $5,678,respectively.The kurtosis and skewness factors for all the three variables further indicatethat distribution is approximately normal (with some measure of skewness).2.Following regression models and equations were obtained for the 2 cases:Case 1: Income as the Independent variableThe regression equation is given as:y=β0+β1(x)Amountcharged($)=2204.24+40.47(Income($1000s))Excel Regression Output:SUMMARYOUTPUTRegression StatisticsMultiple R0.6308R Square0.3979Adjusted R Square0.3853Standard Error731.9025Observations50ANOVAdfSSMSFSig. FRegression116991228.9116991228.9131.720.0000Residual4825712699.11535681.23Total4942703928.02CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept2204.24329.136.6970.00001542.472866.01Income ($1000s)40.477.195.6320.000026.0254.92CommentsThe overall model and the individual slope coefficient are statisticallysignificant (Sig. F and p-value are less than the assumed significance level of0.05).However, the model is a poor fit as it explains only about 39.79% of thevariation in the dependent variable (annual amount charged).Page |2
HI6007 Group AssignmentCase 2: Household size as the Independent variableThe regression equation is given as:Amountcharged($)=2581.64+404.16¿Excel Regression Output:SUMMARYOUTPUTRegression StatisticsMultiple R0.7529R Square0.5668Adjusted R Square0.5578Standard Error620.8163Observations50ANOVAdfSSMSFSig. FRegression124204112.2824204112.2862.800.0000Residual4818499815.74385412.83Total4942703928.02CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept2581.64195.2713.2210.00002189.032974.26Household size404.1651.007.9250.0000301.61506.70CommentsHere as well, the overall model and the individual slope coefficient (householdsize) are statistically significant.Further, the model is a moderate fit as it explains about 56.68% of the variationin the dependent variable (amount charged) by the predictor variable(household size).ConlcusionAs evident from the above models, the variable ‘household size’ is a better predictorof annual credit card charges at it explains about 56.68% of the variation in thedependent variable (more than that by the variable Income).Page |3
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