Statistics

Introduction

Linear Regression Process

The first step in linear regression is to use the data from the sales figures of a retail bakery. The bakery added fat free product and would like compare sale figures to see if there is a difference in the sales after the introduction of at free product. The time period studied is six years. The data is placed in an Excel spreadsheet. The spreadsheet is attached as Appendix A.

The second step for the linear regression process is to plot the information in a scatter diagram. Diagram 1-1 shows the results of the sales of the bakery.

Diagram 1-1

At first glance, the diagram shows there is not a lot of difference between the two sets of information even with a product offering for the health conscience consumer.

To understand the diagram better, we need to determine the coefficient of correlation. The coefficient of correlation describes the strength of the relationship between the two sets of information. It can assume a value from a -1.0 to +1.0 inclusive (Lind, Marchal, & Wathen, 2004). The closer the coefficient of correlation is to -1.0 or + 1.0 the closer the relationship is between the two variables. Microsoft Excel provided the tool to find the coefficient of correlation. The results from that test show the coefficient of correlation from our data set to be 0.993.

Regression analysis is a technique that examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). Regression analysis can be used as a descriptive method of data analysis (such as curve fitting) without relying on any assumptions about underlying processes generating the data (Malpa & McPhillips, 2008).

The results are derived from a systematic method of relating the dependent variable (one to be explained) to the explanatory variables (regressors). The results of regression analysis are significant to a company because they help in the process of forecasting future data, hypothesis testing, and in the modeling of one relationship to another. By using various statistical measures, a company can also use regression analysis as a business plan tool to assist in forecasting project results and survey data. Regression analysis results are also significant to a company because they aid in determining economic significance. One of the most notable ways that regression analysis is significant to a company is that of how it plays a major role in customer satisfaction. According to Quirks.com, "Regression analysis can pinpoint the areas that have the greatest impact on customer satisfaction. It is effective in illustrating the impact on performance one product or service issue (independent variable) has on overall customer satisfaction (dependent variable) with the company" (Malpa & McPhillips, 2008). Companies can benefit from this because they may be better able to identify how to utilize their resources. This could help a company maintain profitability and ultimately help to ensure long-term success.

By using the regression formula to analyze the data available from the sales of the bakery department compared with the sales of those products that are aimed at the fat free market it becomes clear whether there is truly and increase in the demand and purchase of fat free products. The formula shows the results of the sales. The following is the graphs worked from the statistics available regarding quarterly sales.

Regression Analysis

rÐ'І 0.986 n 12

r 0.993 k 1

Std. Error 3.719 Dep. Var. Sales w/fat free prdt (y)

ANOVA table