revision

[Type text] [Type text] [Type text]

7

Regression Analysis Report

Trident University

Teresa A. Coward/ ID M0000318024

Module 2 Case 2

BUS520: Business Analytics and Decision Making

Professor Dr. David Fogarty

January 29th, 2018

What To Know

As one of the consultants for the Diligent Consulting Group, I had previously completed the initial project for our client, the ABC Furniture Company, which was comprised of developing and testing a forecasting method which uses linear regression as a technique to simplify and give direction on how we go about moving forward in understanding the relationship between the consumers who visits the stores and the related sales associated with this collected customer traffic data. In this report, we’re going to analyze a case study, in which my role as lead consultant of D.C.G; other clients like the New Star Grocery Company, who also trusts that there might be a connection between the quantity of clients and the aggregate deals for consumer volume for the given time frame in the same month has financial similarity. To test this examination, the customer information in the course of current numerical vales in the recent months and on a month to month basis for the duration of the same year

Statistical Analysis

Statistics is the field of scientific examination and investigation thats utilized for making sense of the models, for example, linear models, exponential models, logarithmic models and more others, in representing and or making summations about information or real world real-time investigations. One of the most usual applications of Statistics is describing a set of data using estimation. By analysing and examining the raw data, we can make and draw logical conclusions or even compare, contrast or rank of the data on the specified attribute. Evaluating the status of your business by considering its attributes that affect customers is a very important aspect for the growth and development of any business establishments. (Walpole, 1982)

The mean error is an informal term that usually refers to the average of all the errors in a set. An “error” in this context is an uncertainty in a measurement, or the difference between the measured value and true or correct value. The more formal term for error is measurement error, also called observational error. To analyze this case study, we are creating the linear equation and regression model that will give a clear guideline on the relationship between the various variables that are to be considered for the analysis. And then we come to conclude that how the data relate to one another.

The linear regression makes and attempts to model the relationship between dependent variable and independent variable by fitting a linear equation to observed information. In our case the dependent variable is sales and independent variable is the consumer. These two variables are our main concern all through this analysis report so a clearer and concise picture can be drawn. For example, in my research on this study, we want to relate that the customer and sales using linear regression model will give us a clear flow of this relationship that co-exist between the two mathematically. We will be able to interpret what is really the relationship between the two and therefore from the research standpoint, we can get to a point for a decision to be made for this case truly evaluating the information on just these two variables as a clear outline as the conclusionary route to take for that matter.

Before attempting to fit a linear model to the observed data, a modeler should first determine whether or not there is a relationship between the variables of interest. This is to make sure that the resultant values will give a credible data that can be analyzed and therefore referenced when making any decision that is in connection to the matter at hand. This does not necessarily imply that one variable causes the other. But there is some significant association amongst the two variables. A scatterplot can be a helpful tool in determining the strength of the relationship between two variables. If there appears to be no association between the proposed explanatory and dependent variables (i.e., the scatterplot does not indicate any increasing or decreasing trends), then fitting a linear regression model to the data probably will not provide a useful model. A valuable numerical measure of association between two variables is the correlation coefficient, which is a value between -1 and 1 indicating the strength of the association of the observed data for the two variables.

A linear regression line has an equation of the form, where X is the explanatory variable and Y is the dependent variable. The slope of the line is, and is the intercept (the value of y when x = 0).

The provided in the excel sheet we can see that there are two column one is sales and other one is customer. Here we assume and conclude that:

Dependent variable (Y) = sales

Independent variable (X) = customers

Now we have to fit regression and find scatter plot and analyze and interpret the data.

From the regression and scatter plot the linear equation of the model is. (Excel sheet is attached)

In the equation the slope is 0.648 and the y intercept is 111.65. The interpretation of slope is for one unit change in customers will be 0.648 unit increase in sales. We draw the sector diagram. From that we can conclude that there is positives linear relationship exist bet R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determinations for multiple regressions. From the scatter diagram we also see R-squared values is 0.718. R-squared values indicate that the model explains 71.8 % the variability of the response data around its mean. In general, the higher the R-squared, the better the model fits your data.

Predicting future sales, the equation of the Predicting future sales is the same with linear regression equation.

But from the scatter diagram we also see R-squared values is 1. It is indicates that the model explains all the variability of the response data around its mean. We can test the same hypothesis using overall significance and individual significance. Let suppose Here we want to test the hypothesis that.

Where B is population slope for customers. Assume alpha = level of significance = 0.05

Here for overall significance test statistic follows F-distribution and for individual significance test statistic follows t-distribution.

Here P-value < alpha Reject H0 at 0.05 level of significance. Conclusion of this is the population slope for customers is differing than 0. OR customers are an significant variable.

Conclusion And Recommendation

From all of the above analysis, graphs, regression model, Predicting future sales and R-squared value, we conclude that is significant and positive linear relation exist between customer and sales. We also seen that the linear model explains 71.8% the variability of the response data around its mean and the prediction future model explains 100% the variability of the response data around its mean. We also know that the higher the R-squared, the better the model fits your data. So, I would like to recommend and suggest predicting future sales should be use because of high fitness of the model.

References

Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.

Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd

Frost, J. (1970, May 30). Regression Analysis: How Do I Interpret R-squared and Assess

the Goodness-of-Fit? Retrieved January 23, 2018, from http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

Khan, S. (n.d.). Second regression example. Retrieved January 22, 2018, from

https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/more-on-regression/v/second-regression-example?topic=statistics

Khan, S. (n.d.). Regression line example. Retrieved January 22, 2018, from

https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/more-on-regression/v/regression-line-example?topic=statistics

Linear Regression. (n.d.). Retrieved January 23, 2018, from

http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm

Solutions, S. (n.d.). Assumptions of Linear Regression. Retrieved January 23, 2018, from

http://www.statisticssolutions.com/assumptions-of-linear-regression/

Statistics How To.com. (n.d.). Regression Equation: What it is and How to use it.

Retrieved January 22, 2018, from http://www.statisticshowto.com/what-is-a-regression-equation/