Correlation And Regression Analysis Using Sun Coast Data Set

Correlation and Regression Analysis Using Sun Coast Data Set

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Data Analysis: Hypothesis Testing

In this case study, we are going to use sun coast data remediation data set and conduct a correlation analysis, simple regression analysis, and multiple regression analysis using the correlation tab, simple regression tab, and multiple regression tab respectively. The statistical output tables should be cut and pasted from Excel directly into the final project document. For the regression hypotheses, display and discuss the predictive regression equations.

Correlation:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.601842

R Square

0.362274

Adjusted R Square

.360083

Standard Error

5.518566

Observations

1503

ANOVA

df

SS

MS

F

Significance F

Regression

5

25891.89

5178.378

170.0361

2.1E-143

Residual

1497

45590.49

30.45457

Total

1502

71482.38

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

76.825

0.62382

203.2997

0

125.5988

128.0461

125.5988

128.0461

X Variable 1

-2

4.76E-05

-23.4885

4.1E-104

-0.00121

-0.00102

-0.00121

-0.00102

X Variable 2

0.047342

0.037308

1.268957

0.204654

-0.02584

0.120524

-0.02584

0.120524

X Variable 3

5.49532

2.927962

-1.87684

0.060734

-11.2387

0.248026

-11.2387

0.248026

X Variable 4

0.08324

0.0093

8.950317

1.02E-18

0.064997

0.101482

0.064997

0.101482

X Variable 5

-24.506

16.51903

-14.5593

5.21E-45

-272.909

-208.103

-272.909

-208.103

The value of r-squared has shown that the independent variables account for 74% of variation in the dependent variable. The intercept is the value of dependent variable when the value of all independent variables has been put to zero. The most powerful independent variable is variable 5 which has the highest value of coefficient. The negative sign shows that the increase in variable 5 will result in an increase in the dependent variable and vice versa. The variables having p-values less than 0.05 will reject the null hypothesis whereas other variables will have their null hypothesis accepted ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"VGGgzxfG","properties":{"formattedCitation":"(\\uc0\\u8220{}11. Correlation and regression | The BMJ,\\uc0\\u8221{} n.d.)","plainCitation":"(“11. Correlation and regression | The BMJ,” n.d.)","noteIndex":0},"citationItems":[{"id":311,"uris":["http://zotero.org/users/local/5OlhLovK/items/LNEM9CJG"],"uri":["http://zotero.org/users/local/5OlhLovK/items/LNEM9CJG"],"itemData":{"id":311,"type":"webpage","title":"11. Correlation and regression | The BMJ","URL":"https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/11-correlation-and-regression","accessed":{"date-parts":[["2019",12,9]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (“11. Correlation and regression | The BMJ,” n.d.).

Simple Regression: Hypothesis Testing

Restate the hypotheses:

Ho2: β1 = 0

Ha2: β1 ≠ 0

Enter data output results from Excel Toolpak here.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.939559

R Square

0.882772

Adjusted R Square

0.882241

Standard Error

161.303

Observations

223

ANOVA

df

SS

MS

F

Significance F

Regression

1

43300521

43300521

1664.211

7.7E-105

Residual

221

5750122

26018.65

Total

222

49050644

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1753.602

30.36296

57.75465

2.6E-135

1693.764

1813.44

1693.764

1813.44

X Variable 1

-6.15739

0.150936

-40.7947

7.7E-105

-6.45485

-5.85994

-6.45485

-5.85994

The above table shows that the p-value is less than the significance level of 0.05 which will result in the rejection of null hypothesis that the coefficients are equal to zero. The ANOVA table also supports this conclusion because the significance level is less than 0.05. The intercept shows the value of dependent variable when independent variable is put equal to zero. The value of coefficient for variable 1 shows that that a unit change in this variable will bring a change of 6.15 units in the dependent variable (Zou, Tuncali, & Silverman, 2003)

.

Multiple Regression: Hypothesis Testing

Restate the hypotheses:

Ha3: There is no significant impact of any independent variable on the dependent variable.

Ha3:There is a significant impact of independent variables on the dependent variable.

Enter data output results from Excel Toolpak here.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.601842

R Square

0.362214

Adjusted R Square

0.360083

Standard Error

5.518566

Observations

1503

ANOVA

df

SS

MS

F

Significance F

Regression

5

25891.89

5178.378

170.0361

2.1E-143

Residual

1497

45590.49

30.45457

Total

1502

71482.38

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

126.8225

0.62382

203.2997

0

125.5988

128.0461

125.5988

128.0461

X Variable 1

-0.00112

4.76E-05

-23.4885

4.1E-104

-0.00121

-0.00102

-0.00121

-0.00102

X Variable 2

0.047342

0.037308

1.268957

0.204654

-0.02584

0.120524

-0.02584

0.120524

X Variable 3

-5.49532

2.927962

-1.87684

0.060734

-11.2387

0.248026

-11.2387

0.248026

X Variable 4

0.08324

0.0093

8.950317

1.02E-18

0.064997

0.101482

0.064997

0.101482

X Variable 5

-240.506

16.51903

-14.5593

5.21E-45

-272.909

-208.103

-272.909

-208.103

The above tables show the output for multiple regression analysis. There are some variables which have significant relationship with the dependent variable whereas some variables have insignificant relationship. The variables 2 and 3 have insignificant relationships with the dependent variable and other variables have a significant relationship with it. Thus, we can reject the null hypothesis because it stated that no independent variable will have a significant relationship with the dependent variable ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"FvoAspCN","properties":{"formattedCitation":"(Ken Plummer, 16:36:56 UTC)","plainCitation":"(Ken Plummer, 16:36:56 UTC)","noteIndex":0},"citationItems":[{"id":309,"uris":["http://zotero.org/users/local/5OlhLovK/items/4LQIUM6B"],"uri":["http://zotero.org/users/local/5OlhLovK/items/4LQIUM6B"],"itemData":{"id":309,"type":"speech","abstract":"Null hypothesis for multiple linear regression","genre":"Education","title":"Null hypothesis for multiple linear regression","URL":"https://www.slideshare.net/plummer48/null-hypothesis-for-multiple-linear-regression","author":[{"family":"Ken Plummer","given":""}],"accessed":{"date-parts":[["2019",12,9]]},"issued":{"literal":"16:36:56 UTC"}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} (Ken Plummer, 16:36:56 UTC).

References

ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY 11. Correlation and regression | The BMJ. (n.d.). Retrieved December 9, 2019, from https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/11-correlation-and-regression

Cheusheva, S. (2018, August 1). Linear regression analysis in Excel. Retrieved December 9, 2019, from Excel tutorials, functions and formulas for beginners and advanced users—Ablebits.com Blog website: https://www.ablebits.com/office-addins-blog/2018/08/01/linear-regression-analysis-excel/

How to Run a Multiple Regression in Excel. (n.d.). Retrieved December 9, 2019, from WikiHow website: https://www.wikihow.com/Run-a-Multiple-Regression-in-Excel

Ken Plummer. (16:36:56 UTC). Null hypothesis for multiple linear regression. Education. Retrieved from https://www.slideshare.net/plummer48/null-hypothesis-for-multiple-linear-regression

Zou, K. H., Tuncali, K., & Silverman, S. G. (2003). Correlation and simple linear regression. Radiology, 227(3), 617-628.