Statistics (3 Pages report)

REGRESSION ANALYSIS

Assignment Overview

You are a consultant who works for the Diligent Consulting Group. In this Case, you are engaged on a consulting basis by Loving Organic Foods. In order to get a better idea of what might have motivated customers’ buying habits you are asked to analyze the factors that impact organic food expenditures. You opt to do this using linear regression analysis.

Case Assignment

Using Excel, generate regression estimates for the following model:

Annual Amount Spent on Organic Food = α + bAge

After you have reviewed the results from the estimation, write a report to your boss that interprets the results that you obtained. Please include the following in your report:

1. The regression output you generated in Excel.

2. Your interpretation of the coefficient of determination (r-squared).

3. Your interpretation of the coefficient estimate for the Age variable.

4. Your interpretation of the statistical significance of the coefficient estimate for the Age variable.

5. The regression equation with estimates substituted into the equation. (Note: Once the estimates are substituted into the regression equation, it should take a form similar to this: y = 10 +2x)

6. A discussion of how this equation in item 5 above can be used to estimate annual expenditures on organic food.

7. An estimate of “Annual Amount Spent on Organic Food” for the average consumer. (Note: You will need to substitute the average age into the regression equation for x, the intercept for α, and solve for y.) Data: Download the Excel-based data file:  BUS520 Module 3 Case .

Assignment Expectations

Written Report

Length requirements: 3–4 pages minimum (not including Cover and Reference pages). NOTE: You must submit 3–4 pages of written discussion and analysis.

Provide a brief introduction to/background of the problem, similar to the introduction/background you provided in Module 1 and 2 Case submissions.

Provide a brief discussion of linear regression analysis, including the value of using this estimation technique.

Provide a written analysis that addresses each of requirements listed under the “Case Assignment” section.

Write clearly, simply, and logically. Use double-spaced, black Verdana or Times Roman font in 12 pt. type size.

Please use keywords as headings to organize the report.

Avoid redundancy and general statements such as "All organizations exist to make a profit." Make every sentence count.

Paraphrase the facts using your own words and ideas, employing quotes sparingly. Quotes, if absolutely necessary, should rarely exceed five words.

Upload both your written report and Excel file to the Case 3 Dropbox.

Title: Statistics Project – Regression Analysis

Name:

Date:

Introduction

I am a consultant working for the Diligent Consulting Group. The consultation exercise, for this case, was conducted on an organization called “Loving Organic Foods.” To get a better understanding of what could be motivating the buying habits of customers, I was tasked with the responsibility of analyzing the factors that impact expenditure on organic foods. To achieve that feat, I have opted to use a linear regression analysis.

Data description by the use of regression is one of the most popular applications of statistics when provided with a set of data such as that on Diligent Consulting Group. Through analysis and examination of the raw data, we are able to make and arrive at logical conclusions, compare and contrast, or even classify the data (or establishments) based on the attribute of specification.

The application of regression statistical methods is among the most effective ways of properly examining these attributes. Among other things, one might find the need to apply the concepts of correlation as well as linear regression equations. Once enough data is gathered and analyzed, it will be possible for one to identify the attributes with the most significant data and those with the least significant data. The focus of this paper thus, is regression (Walpole, 1982).

Below are the answers to the questions asked.

Before going to analyze the data I would like to explain the variables.

In this case two variables are given; Annual Amount Spent on Organic Food, and Age, where the independent variable is Age, while the dependent variable is the Annual Amount spent on Organic Food.

The descriptive summary of both variables is given below:

The descriptive summary shows that the average of Annual Amount Spent on Organic Food is 11046.48 and average is 48.23 years/

Variable number of age is little bit.

Regression and Scatter Plot Analysis

The Scatter Plot

From the regression table and scatter plat we can easily conclude the regression equation which is:

Where y represent Annual Amount Spent on Organic Food and x represent age.

The slope of the equation, 26.293, tells us that increasing one’s age leads to an increase of the Annual Amount Spent on Organic Food by 26.293 and the y intercept, 9778.277 is the initial Annual Amount Spent on Organic Food.

Additionally, R-squared statistically measures the closeness of the data to the fitted line of regression line. The R Square is 0.013, which means that the model describes 1.3% of the changeability of the response data based on its mean. Correlation coefficients are used to measure how strong the relationship between two variables are. The coefficient of correlation is the square root of the R-squared value.

The correlation coefficient of 0.114 shows that there is a weak positive relationship between Annual Amount Spent on Organic Food and Age.

Since there are p-values corresponding Age (0.204) >0.05, their presence in this regression model is insignificant, leading us to the conclusion that no strong relationship exists between Annual Amount Spent on Organic Food and Age. Furthermore, the variable age is statistically insignificant based on the coefficient of correlation.

No let assume

Conclusion

In conclusion, I would like to say that no strong relation exists between Annual Amount Spent on Organic Food and Age, and the coefficient of determination =0.013 i.e. this regression explains that there is a 1.3% of total variation in the sample of Annual Amount Spent on Organic Food. When there is a one-unit increase in the Age variable while keeping the other independent variables constant, there is a 26.239-unit increase in the Annual Amount Spent on Organic Food.

References

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

Reid, H. (2013, August). Introduction to Statistics. SAGE Publication.

The above reference needs to appear in the text as an APA citation.

Annual Amount Spent on Organic FoodAge

Mean11046.4838748.23387

Standard Error334.81369331.463298

Median1119846.5

Mode1080038

Standard Deviation3728.32749916.2946

Sample Variance13900425.94265.514

Kurtosis-0.811935981-1.11557

Skewness0.1520192090.12932

Range1537357

Minimum280021

Maximum1817378

Sum13697645981

Count124124

SUMMARY OUTPUT

Regression Statistics

Multiple R0.115

R Square0.013

Adjusted R Square0.005

Standard Error3718.777

Observations124

ANOVA

dfSSMSFSignificance F

Regression122577100.13822577100.1381.6330.204

Residual1221687175290.83013829305.663

Total1231709752390.968

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept9778.2771047.2349.3370.0007705.17311851.3827705.17311851.382

Age26.29320.5781.2780.204-14.44367.029-14.44367.029