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Regression Analysis Reporting II

Trident University

Teresa A. Coward/ ID M0000318024

Module 2 SLP 2

BUS520: Business Analytics and Decision Making

Professor Dr. David Fogarty

January 29th, 2018

Overview

I’m a consultant for the Diligent Consulting Group, previously completed the initial project for our client, which was comprised of developing and testing a forecasting method that used linear regression techniques. This method used monthly year one sales over a twelve-month period to forecast year two sales. The ABC Furniture Company believed that the number of patrons who visit their store during any particular month was in relation to the total number of sales for that given month in question. More specifically, the client believed that there was a positive relationship between higher customer traffic in the store and higher total sales associated with consumer commerce, i.e. the client believed that the higher the number of customers who visited the store, the higher the total sales would be.

The client had provided me with the number of customers who visited the store over the most recent twelve-month period from January to December, with the sales corresponding to each of those months. A linear regression equation was obtained using this client’s collected information. The linear regression equation was then used to forecast the sales for year two. The forecast sales were later compared with the actual year two sales. In this case the comparison was meant to obtain the trend with which the performance in this docket was moving. This is an analytical move that is used in obtaining for example variances for analysis purposes and ultimately making a decision.

Statistical Evaluation

When factual information is used to scientifically examine closely data by utilizing linear, logarithmic or exponential models for representations and make for certifiable investigations. The information gathered acts as a motivator behind basic leadership decisions. In this manner, for our situation we will utilize the factoring principle where the data is concerned and negate through the research, taking a gander at all the different issues that needs to be address that are concerns of management, from those suggestions steer to a comprehension of these different factors connecting together for a solution. One of the most usual applications of statistics is describing a set of data using estimation. By anlizing thus throughly examining the raw data, we can make and draw a logical conclusion or even compare, contrast or rank of the data on the specified attribute. This helps us to make a clear analysis of the data at hand and therefore come up with clear understanding of this correlation between the two, therefore coming to a sound decision in the end accordingly. Evaluating the status of your business by considering its attributes that affect customers is a very important aspect for growth and development, of any business establishments (Walpole, 1982). As a manager or any other executive for consideration with the mandate of managing the existence and operations of the business, the understanding of the foresaid variables relationship is a crucial thing that needs not be ignored. My research will show this, as far as wanting the corporation to go far as far as performance and economic visibility are concerned.

According to Statistics How To.com; “the mean error is an informal term that usually refers to the average of all the errors in a set. In dissecting this case study, we are creating the linear equation and regression model that will give us a clear relationship between our independent and dependent variable. First, we’ll calculate in excel the mean error and then we’ll streamline to viable conclusion, as quoted from Statistics How To.com; an “error” in this context is an uncertainty in a measurement, or the difference between the measured value and true/correct value. The more formal term for error is measurement error, also called observational error. How the data relate in regard to the correlation that the two variables have, the value expected from the same correlation and the behavior of the regression line. The linear regression makes an effort to model the affiliation between supported variable and objective variable by fitting a linear equation to observed this figures. In our case the dependent variable is sale and independent variable is the consumer.

The mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.

The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics, for example in trend estimation, as it usually expresses accuracy as a percentage.

Value Calculation Forecast

Endeavoring to fit all raw data for value review, applicable information in this technique once the determination of the association between not standing more on the opposition that one variable causes the other. 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. This portion of the research we’ll assume and conclude that

Dependent variable (Y) = sales, the Independent variable (X) = customers hence we have to fit regression and find scatter plot and analyze as well as 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.

Mean absolute percentage error calculation.

And for SES – MAPE for alpha = 0.15

And for SES – MAPE for alpha = 0.9

Now 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. Deduction, the population slope for customers is different than 0. Or consumers are significant variable.

Concluded Recommendation

After diligent research and as your consultant for the Diligent Consulting Group, I’ve completed the analysis as well as finalized the forecasting by the two methods; fist Linear Regression (LR) and Single Exponential Smoothing (SES) to forecast sales. Therefore, I have been able to categorize the relationship between our two main identified variables in this case; consequently, my proposal is as follows:

My recommendations as I’ve come to understand through my research, is that the mean absolute percentage error is 6.620 for Single Exponential Smoothing method and the mean absolute percentage error is 17.736 for forecast method. Simply, I’ve concluded that the lowest mean absolute percentage error is better to use and suggested which Single Exponential Smoothing method.

References

CONTENT TEAM, A. (2016, July 14). Going Deeper into Regression Analysis with

Assumptions, Plots &

Downie, N. M. & Heath, R. W. (1965). Basic Statistical Methods (2nd ed.). Harper &

Row Publishers

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/

Walpole, R. (1982). Introduction to Statistics. (3rd ed.). Prentice Hall Publication.

(2016, January 22). Retrieved January 23, 2018, from

[Typetext] [Type text] [Type text]

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/

REPORT 2

by Ass 2 Ass 2

Submission dat e : 30- Jan- 2018 06:38AM (UT C- 0800)
Submission ID: 9087 317 85
File name : Linear_Ref ressio n_Case_2_by_T eresa_Co ward.do cx (52.24 K)
Word count : 1360
Charact e r count : 7 692

56%
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32%
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21%
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53%
ST UDENT PAPERS

1 11%
2 10%

3 6%

4 4%
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6 2%
7 2%

REPORT 2
ORIGINALITY REPORT

PRIMARY SOURCES

Submitted to Trident University International

St udent Paper

Submitted to Colorado Technical University
Online
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Submitted to American Public University
System
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www.statisticshowto.com
Int ernet Source

Submitted to Southern New Hampshire
University – Continuing Education
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swdllc.paresspacewarpresearch.org
Int ernet Source

Submitted to American Intercontinental
University Online
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Submitted to Laureate Higher Education Group

2%
9 2%
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brainmass.com
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cc.msnscache.com
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Submitted to Belhaven University
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Submitted to Oklahoma State University
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Submitted to Saint Joseph’s Institution,
Singapore
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Submitted to University of Witwatersrand
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Submitted to Manchester Metropolitan
University
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en-mat.com
Int ernet Source

blog.minitab.com
Int ernet Source

19 1%

Exclude quo tes Of f

Exclude biblio graphy Of f

Exclude matches Of f

Hamed Fazlollahtabar, Mohammad Ali Ehsani.
“Integration between Regression Model and
Fuzzy Logic Approach f or Analyzing Various
Electronic Commerce Ef f ects on Economic
Growth in Organizations”, Journal of Electronic
Commerce in Organizations, 2010
Publicat ion

REPORT

by Assignment 1 Asssignment 1

Submission dat e : 30- Jan- 2018 06:37 AM (UT C- 0800)
Submission ID: 9087 314 35
File name : Linear_Regressio n_SLP_2_by_T eresa_Co wad.do cx (50.98K)
Word count : 1296
Charact e r count : 7 133

48%
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27%
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14%
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42%
ST UDENT PAPERS

1 14%
2 12%
3 4%
4 3%
5 3%

6 3%
7 2%

REPORT
ORIGINALITY REPORT

PRIMARY SOURCES

brainmass.com
Int ernet Source

Submitted to Trident University International
St udent Paper

www.statisticshowto.com
Int ernet Source

www.internationalresearchjournalof f inanceandeconomics.com
Int ernet Source

Submitted to American Public University
System
St udent Paper

www.ref erence.com
Int ernet Source

Luca Gugliermetti, Gianf ranco Caruso, Luca
Saraceno. “Prediction of subcooled f low boiling
pressure drops in small circular tubes”,
International Journal of Heat and Mass
Transf er, 2017
Publicat ion

8 2%

9 1%
10 1%

11 1%
12 1%
13 1%

Exclude quo tes Of f

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Submitted to American Intercontinental
University Online
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Submitted to University of Witwatersrand
St udent Paper

Li, Xuejiao, and Takashi Hibiki. “Frictional
pressure drop correlation f or two-phase f lows
in mini and micro single-channels”,
International Journal of Multiphase Flow, 2017.
Publicat ion

hec.gov.pk
Int ernet Source

www.jolst.net
Int ernet Source

FINAL GRADE

REPORT
GRADEMARK REPORT

GENERAL COMMENTS

Instructor

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