Applied Managerial Statistics

GM 533: Applied Managerial Statistics

Felix Fair

12/17/2012

Professor Charles Trinkel

Project Part C

Summary Report

AJ Davis Department Store wants a random sample performed on 50 customers based on location, income, family size, and credit. The information provided in this study is needed so that AJ Davis can have a clearer idea of their customers spending habits based on the variables that have been made available . The correlation coefficients of the variables reveal and identify direct relationships. In doing so we are able to clarify that there is an extremely low chance that credit balances are due to chance. We are also able to utilize independent variables of income and size as significant contributions. This also allows for the variable of Years to be discarded because it does not have a significant contribution.

The conclusion that was determined along with and because of the analysis, Is summarized that income and size are good predictors that credit balances will increase. This information and the identification of these relationships are important to AJ Davis Department Store and enhance their ability to improve their current model. The following statistics show how AJ Davis Department store will be able to thrive..

Using MINITAB perform the regression and correlation analysis for the data on CREDIT

BALANCE (Y) and SIZE (X) by answering the following.

1. Generate a scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the 'best fit' line. Interpret.

From the scatter plot it is evident that the slope of the 'best fit' line is positive, which indicates that Credit Balance varies directly with Size. As Size increases, Credit Balance increases and vice versa.

MINITAB OUTPUT:

Regression Analysis: Credit Balance($) versus Size

The regression equation is

Credit Balance($) = 2591 + 403 Size

Predictor Coef SE Coef T P

Constant 2591.4 195.113.290.000

Size 403.22 51.00 7.910.000

S = 620.162 R-Sq = 56.6% R-Sq(adj) = 55.7%

Analysis of Variance

Source DF SS MS F P

Regression 1 24092210 2409221062.640.000

Residual Error 48 18460853384601

Total 49 42553062

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI

1 4607.5119.0 (4368, 4846.9) (3337.9, 5877.2)

Values of Predictors for New Observations

New Obs Size

1 5.00

2. Determine the equation of the 'best fit' line, which describes the relationship between CREDIT BALANCE and SIZE.

The equation of the 'best fit' line or the regression equation is

Credit Balance ($) = 2591 + 403.2 Size

3. Determine the coefficient of correlation. Interpret.

The coefficient of correlation is given as r = 0.752. The positive sign of the correlation coefficient indicates a positive or direct relationship between the variables. The correlation coefficient is far from the P-Value of 0.000, P-Value of 0.000 is low. This means that there is an extremely low chance that Credit Balance and Size results are due to chance.

MINITAB OUTPUT:

Pearson correlation of Credit Balance ($) and Size = 0.752. P-Value = 0.000

4. Determine the index of determination. Interpret.

The index of determination, r-square = 0.566. The proportion of variability in a dataset that is accounted for by the regression model is given by the coefficient of determination R^2, which for this regression model is 56.6%.

MINITAB OUTPUT;

S = 620.162 R-SQ = 56.6% R-SQ(adj)= 55.7%

5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including the p-value.

The null hypothesis,H_0 states that there is no significant correlation, or the correlation coefficientρ=0.

Significance Level, α = 0.05

Decision Rule: RejectH_0 ifthep-value< 0.05 (significancelevel,alpha)

From the ANOVA table, we find that the p-value 0.000is much less than 0.05. Therefore, we reject the null hypothesis that there is no significant correlation and conclude that, according to the overall test of significance, the regression model is valid.

MINITAB OUTPUT:

Analysis of variance

Source DF SS MS F P

Regression 1 24092210 24092210 62.64 0.000

Residual Error 48 18460853 384601

Total 49 42553062

6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.

Size is a very good predictor of Credit Balance. As Size increase Credit Balance increases and they are correlated. Therefore, as the Size of the household grows so does the Credit Balance of those households.

7. Compute the 95% confidence interval for β. Interpret this interval.

The 95% confidence interval for β is given as (301.59, 506.67). If repeated observations