Statistics (3 Pages report)

 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.
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:
The regression output you generated in Excel.
Your interpretation of the coefficient of determination (r-squared).
Your interpretation of the coefficient estimate for the Age variable.
Your interpretation of the statistical significance of the coefficient estimate for the Age variable.
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)
A discussion of how this equation in item 5 above can be used to estimate annual expenditures on organic food.
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: I can provide this file
Written Report
Length requirements: 3 pages minimum (not including Cover and Reference pages). NOTE: You must submit 3 pages of written discussion and analysis.

Sheet2

,

d, and the R squared adjusted for degrees of freedom, which is the one you want to report. You also get the Standard error (of the estimate) and the number of observations in the regression.
The second block of information is titled

which stands for Analysis of Variance. Our interest in this section is the column marked

. This is the calculated F statistics for the null hypothesis that all of the coefficients are equal to zero verse the alternative that at least one of the coefficients are not equal to zero. This hypothesis test was presented in

3.4 under “How Good is the Equation?” The next column gives the p value for this test under the title “

”. If the p value is less than say 0.05 (the calculated F statistic is in the tail) we can say with 90 % confidence that we cannot accept the null hypotheses that all the coefficients are equal to zero. This is a good thing: it means that at least one of the coefficients is significantly different from zero thus do have an effect on the value of Y.
The last block of information contains the hypothesis tests for the individual coefficient. The estimated coefficients, the intercept and the slopes, are first listed and then each standard error (of the estimated coefficient) followed by the t stat (calculated student’s t statistic for the null hypothesis that the coefficient is equal to zero). We compare the t stat and the critical value of the student’s t, dependent on the degrees of freedom, and determine if we have enough evidence to reject the null that the variable has no effect on Y. Remember that we have set up the null hypothesis as the status quo and our claim that we know what caused the Y to change is in the alternative hypothesis. We want to reject the status quo and substitute our version of the world, the alternative hypothesis. The next column contains the p values for this hypothesis test followed by the estimated upper and lower bound of the confidence interval of the estimated slope parameter for various levels of confidence set by us at the beginning.

Statistics

Multiple R

1

R Square

0

9

16

01

8.

7

19209

ANOVA

F Significance F

Regression 1

7100.1

9118

22577100.1379118

25

8577

9795

7175

0.82983

29

5.

25

6

9752390.9

Standard Error

.

7

3

92

.2

8884

2

12

90938241202E-16

2

7705.1733

3258 11851.3815019326

637

0.20377

795

36

-14.4434192796 67.0291405536

											SUMMARY OUTPUT	Once the data are entered and the choices are made click OK and the results will be sent to a separate new worksheet by default. The output from Excel is presented in a way typical of other regression package programs. The first block of information gives the overall statistics of the regression:	Multiple R	R Square	ANOVA	F	1	Significance F
	Regression
0.11	49		25		52
0.01		32				48		46
Adjusted R Square	0.00	51				41
	Standard Error	3	71	77			44
Observations	1				24
df	SS	MS
	22					57	37	1.	63		54		0.2037			75
Residual	122	1			68		29	1						38		30			66		39
Total	1				23	1				70	67		74
Coefficients	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	97			78		27			42		62	10			47	33		40	9.33	72			43		36	5.		73		7705.173					34	53				58		11851.38150193	26		45
	Age	26.29			28		60	20.5780371879	1.2777147012	59		-14.4434192796		67.029140	55

Sheet1

Age

77

47

23

38

58

44

34

75

32

39

65

48

85

48

70

49

57

71

47

47

28

63

24

10800 66

24

38

54

28

58

27

48

26

52

29

75

45

74

56

30

57

41

23

28

23

45

33

42

39

60

57

41

67

73

57

64

24

25

34

78

34

34

41

62

57

23

78

36

44

75

70

38

65

68

48

24

46

43

58

66

68

74

32

61

42

60

64

53

62

78

44

58

27

68

21

70

38

25

30

70

37

40

29

54

52

65

72

40

36

43

38

73

41

35

21

59

56

42

46

34

70

55

38

51

66

43

Annual Amount Spent on Organic Food
7348
11598
9224
12991
1			65		56
11515
10469
17933
18173
12305
9080
9113
	61
		64
6000
6760
8579
7393
8161
	10800
6160
8543
17666
12644
14308
9737
13301
18106
11468
9547
7812
155		21
7598
7783
17737
7824
6552
11232
6540
4200
7225
5370
4476
2800
7839
3472
8854
8900
12791
12712
13321
8802
14369
7908
17840
15107
12070
6389
6606
6291
7425
11436
7612
7515
13115
11870
8450
16324
9331		35
9184
16803
10709
14456
16634
12227
13476
14554
9393
14594
6628
11240
13101
14034
17837
7849
10578
11325
7105
16460
8390
14956
10903
12054
11697
12781
17456
12835
13403
15051
14225
11196
11475
5605
9890
13227
11200
9600
15703
6486
9430
7755
8100
14821
10650
12589
11600
13000
17065
16500
8600
11900
16723
16759

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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