# **A Complete SPSS Case Study using Two-Way ANOVA and Regression - SPSS Help**

__Background Information__

BuyEasy is a catalogue retailer of gift items. Its business comprises primarily of sending catalogues to potential customers to solicit sales. Its operations are relatively simple. It has a large warehouse for its impressive range of inventory, ranging from stationery sets and stuffed toys to handphones and MP3 players. The warehouse also serves as a sales and distribution centre to receive orders through its telephone hotlines and to courier ordered goods to its customers.

The remaining part of BuyEasy is a large administrative department, comprising functional sections such as accounting and finance, human resources and marketing. This project involves the marketing section which does substantial marketing research on customer purchasing patterns.

__Business Issues__

BuyEasy is currently preparing for a special Christmas promotion campaign. Among other things, it wants to generate more information before deciding on the important parameters of the campaign.

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For the past several years, BuyEasy has set aside a non-trivial budget to encourage its customers to be Premier members by paying a nominal one-time fee. Such members are entitled to special promotions and discounts. It is expected that Premier members purchase more gifts than non-members, on average. However, there has not been any statistical analysis to empirically test this expectation.

Given the nature of the gifts in the catalog, BuyEasy also believes that customers who are married with children are likely to make more purchases as compared to those who are single or who are married but not have children. This belief has also not been empirically tested via statistical analysis.

__Data__

The marketing section has accumulated a database of 1,000 of its customers. The following variables (comprising transactional data and demographic characteristics) have been captured in the database:

1. idnum = identification number

2. expend = average expenditure per month

3. numpur = average number of purchases per quarter

4. age = age of customer

5. gender = gender of customer

6. income = annual income of customer

7. race = race of customer

8. marital = marital status of customer

9. member = whether customer is a Premier member

More information can be found in the SPSS data set “project_data.sav”.

__Task #1 (ANOVA)__

BuyEasy is interested to find out if and how the average number of purchases per quarter (i.e., numpur) may be associated with the customer’s marital status (i.e., marital) and Premier membership status (i.e., member). Further, BuyEasy is interested to know if there is an interaction effect between marital status and Premier membership status.

The marketing section has employed a statistical consultant to do the above analysis. You are the consultant engaged by BuyEasy.

__Task #2 (Multiple Regression)__

To further plan for its Christmas promotion campaign, BuyEasy wants to know the determinants of the average expenditure per month (i.e., expend). In particular, it wants to know if and how this dependent variable may be associated with demographic independent variables such as the customer’s age, gender, income, marital status and Premier membership status.

In addition to the above (i.e., as a separate analysis), since preliminary results show that gender is not statistically significant, BuyEasy wonders if there may be a significant gender*age interaction effect instead.

Again, you are the consultant engaged by BuyEasy to perform the above analyses.

__Task #3 (ANOVA and Multiple Regression)__

The marketing section is keen to know how business issues and problems can be addressed using ANOVA and multiple regression. In particular, it has asked you to list two examples of business applications using ANOVA and another two examples of business applications using multiple regression.

**MEMO**

The purpose of the following analysis is to provide statistical analysis to be able to answer the managerial questions stated, related to the demand for BuyEasy products and the demographics of its clients. The main issues that need to be addressed are:

• **Task 1: **The relationship between the quarterly quantities of purchased products and factors such as marital status and membership status, as well as the possible interaction between these factors.

• **Task 2: **The determinant factors of the average expenditure per month. In particular, it needs to be determined whether this dependent variable may be associated with demographic independent variables such as the customer’s age, gender, income, marital status and Premier membership status.

• **Task 3: **Specify other business issues that can be addressed by using similar statistical techniques (such as ANOVA and Multiple Regression)

__SPSS Data__

__SPSS Data__

The marketing section has accumulated a database of 1,000 of its customers. The following variables (comprising transactional data and demographic characteristics) have been captured in the database:

1. idnum = identification number

2. expend = average expenditure per month

3. numpur = average number of purchases per quarter

4. age = age of customer

5. gender = gender of customer

6. income = annual income of customer

7. race = race of customer

8. marital = marital status of customer

9. member = whether customer is a Premier member

__Task 1__

In order to address the first task, two-way ANOVA is the analysis that needs to be performed. With the result of a factorial analysis we will be able to determine which factors are significant, and whether the interaction is significant.

The following table shows the results of applying Levene’s Test for homogeneity of the variances:

o The test is significant (\(p = 0.029\)), which means that we reject the null hypothesis across groups. This hypothesis is required for ANOVA, but even when it is not satisfied, ANOVA delivers robust results, most of the cases.

The next table shows the significance of the factors and interactions of the model.

o The above table shows that *Marital Status *is a significant factor (\(p = 0.000\)), but *Membership* is not significant (\(p=0.746\)). The interaction between these two factors is significant (\(p = 0.020\)).

o This implies that the mean number of purchases per month differs significant across the different groups for the variable *Marital Status*, as well as for the interaction between marital status and membership.

o Since there is a difference among groups, it is required to perform Post-Hoc analysis.

o The table above shows the Post-Hoc analysis for the differences. The values marked with (*) show the difference that are significant

o We use Dunnet T3 (because we have unequal variances). The results show that the three groups Single, Married and Married with children have significantly different mean quarterly purchases. This difference is reflected in the following graph:

__Conclusions:__ *Marital status* is significant predictor, which means that families with children bring more sales that single clients. On
the other hand, *Membership *is not significant. This means that there is not a significant difference in the mean quarterly purchases for member and non-members. This is something that should be addressed by the marketing department.

__Task 2__

For this task we need to perform a Multiple Regression analysis to estimate the coefficients of the model

\[Expend={{\beta }_{0}}+{{\beta }_{1}}age+{{\beta }_{2}}gender+{{\beta }_{3}}income+{{\beta }_{4}}marital+{{\beta }_{5}}member+\varepsilon \]

To this end, we will use the least squares method, with the data provided. The results are shown on the table below:

o The table above shows that the correlation coefficient is equal to \({{R}^{2}}=0.867\), which indicated a good linear fit. The coefficient of determination is equal to \({{R}^{2}}=0.751\), which implies that approximately 75.1% of the variance of the dependent variable is explained by the linear regression in the predictors.

o The table above shows that *Age, Income *and *Marital Status *are significant predictors of the model (all with \(p = 0.000\)). The variables *Gender *(\(p = 0.838\)) and *Membership *(\(p = 0.525\)) are *not significant, *at least at the 0.05 significance level.

**Analysis of Residuals**

The chart below show evidence that the linear model is valid

o __The interaction Gender*age__

Now we need to estimate the following model:

\[Expend={{\beta }_{0}}+{{\beta }_{1}}age+{{\beta }_{2}}gender*age+{{\beta }_{3}}income+{{\beta }_{4}}marital+{{\beta }_{5}}member+\varepsilon \]

The variable *Gender *is not included because the previous analysis showed it is not significant. The Multiple Regression is shown below:

o The table above shows that the correlation coefficient is equal to \({{R}^{2}}=0.867\), which indicated a good linear fit. The coefficient of determination is equal to \({{R}^{2}}=0.751\), which implies that approximately 75.1% of the variance of the dependent variable is explained by the linear regression in the predictors. These indicators are exactly the same for as the case with the variable *Age *in the model.

o The table below shows the estimated coefficients and their respective significances.

o The model is

\[E\widehat{xpe}nd=-181.173+5.669age-0.025gender*age+0.738\text{ }income+27.172\,marital-3.183\text{ }member\]

o The variables *Age, Income *and *Marital Status *are significant (\(p=0.000\)). Again, *Membership *(\(p = 0.523\)) is not significant, same as the interaction *Gender*Age* (\(p = 0.807\))*.*

### Conclusions from the SPSS Analysis

*Age *is not a significant predictor of *monthly sales.* *Membership* again is not a significant contributor in the average monthly sales.

__Task 3__

ANOVA and Multiple Regression can provide a wealth of possibilities in terms of business applications. But there is no free lunch, though. The use of statistical analysis must be paired with an appropriate statistical design.

Examples of business applications:

o ANOVA:§ It can be used to analyze the response of different marketing strategies. For instance, three different catalog models could be sent to potential customers, and that way it would be possible to determine what kind of catalog generates more sales, if any

§ It can be used on the Human Resources department, to analyze employee performance. For instance, we could think of factors that can improve the employee’s performance, like training and monetary incentives. ANOVA can help to determine whether different levels of these factors have an influence in the employee’s performance.

o Multiple Regression:

§ It can be used to explore relationships between the data; like in this project we analyzed *Expenditure* versus a series of demographic factors. For instance, we could be interested in finding what demographic factors affect the customer satisfaction.

§ It can be used to determine the *marginal contribution *of each significant factor. This means that we can know how much it would the dependent variable would get affected with the increase in one unit of any of the independent variables

__CONCLUSIONS:__

Membership is not a significant predictor of the monthly expenditure. This means that either the marketing efforts haven’t been enough or maybe the concept is not clear to the prospective clients. It would be recommended to perform further tests to determine whether different initial fees, or different benefits for being a premium member get reflected in the monthly expenditure.

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