Elements of Statistics II

Module 6:  Discussion Forum: Correlation and Simple Linear Regression

Guiding question: After you have done the readings and research on correlation and simple linear regression, answer the following premise explaining in detail your answer: Why is it important to test the significance of the slope in the simple linear regression model?

· Support your answer with specific references according to your readings, using the latest edition of the APA format.

· Include an example, definition, or application of the concept in daily life or work environment.

· Enrich the content of your classmates with information or examples that help in the understanding of the concepts and practices of statistics.

General Instructions for the Discussion Forum

1. Post your answer as established by your instructor on the course calendar. Your comments must be written in your own words. You can offer examples and quotes to support your proposals. Citations of other authors must be properly documented (author's name, title, date, etc.).

2. Post your comments to the response of at least two (2) of your classmates on or before the day set by your instructor on the course calendar. Your reaction may be based on personal experiences, study material, or additional information obtained from the  Online Library (Links to an external site.)  or others, and may include:

· Some understanding received from what is published that synthesizes the information and offers new perspectives or suggestions.

· The validation or rejection of the idea (supported by your experience or research). 

· New information that broadens, adds or contrasts perspectives (based on reading and evidence). 

3. Remember that your work must be original and must not contain material copied from books or the internet. You must respect the intellectual property of the authors and not commit plagiarism.

4. Examine the criteria used to evaluate your assignment to find out how to get the highest grade for your work. The assignments are graded or evaluated through rubrics or by the distribution of points.

5. Before submitting your entry, read your message several times. This will ensure that it contains the exact information you want to communicate.

 

Remember to review the  academic expectations  for your submission.

Submission Instructions:

· Submit your initial discussion post by 11:59 PM Eastern on Wednesday.  

· Contribute a minimum of 350 words for your initial post. It should include at least 2 academic sources, formatted and cited in APA.

· Respond to at least two of your classmates' discussion posts by 11:59 PM Eastern on Sunday. Ask a question, and provide a different viewpoint.

 

Module 6:  Correlation and Simple Linear Regression

Correlation and Simple Linear Regression Summary

A correlation exists between two variables when the values of one variable called dependent variable “y” are related with the other variable called independent variable “x”. The correlation between the two variables is measured by the correlation coefficient “r”.

The correlation coefficient varies from [-1, 1]

r = -1 represents a perfect inverse correlation (negative correlation)

r = 1  represents a perfect positive correlation (positive correlation)

A linear correlation exists between two variables when there is a correlation and the plotted points (x, y) presented in a scatterplot result in a pattern that can be approximated by a straight line.

Scatterplots examples:

(Triola, 2018)

Regression Analysis : Is a collection of statistical tools for finding estimates of the parameters in the regression model.

Correlation:  Measure of linear association (r) 

�=�(∑�⋅�)−(∑�)⋅(∑�)�(∑�2)−(∑�)2�(∑�2)−(∑�)2

Regression Equation:

bo: y-intercept of the regression equation

b1: Slope of the regression equation

Hypothesis Testing

Ho: β1 = 0

H1: β1 ≠ 0

Reject Ho if p-value < Significance Level ( α  )

Failure to reject Ho is equivalent to concluding that there is no linear relationship between “x” and “y”

References:

Rajaretnam, T. (2016).  Statistics for social sciences. Sage Publications, Inc. ISBN-13: 9789351506560

Triola, M. F. (2018).  Elementary statistics (13th ed.). Pearson. ISBN-13: 978-0134462455  https://librarylogin-carolina.uagm.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=e000xww&AN=1214457&site=ehost-live&ebv=EB&ppid=pp_Cover

 

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Module 6:  Correlation and Simple Linear Regression - 2

Scatter Plot or Dispersion Diagram: Is a visual representation of the two variables (X, Y)

Linear Regression Hypothesis Testing

Example of Regression Analysis using Scatter Diagram and Excel Data Analysis

X	Y
1	14
2	33
3	40
4	63
5	76
6	85

Scatter Plot Diagram

Y = bo + b1 X

bo: Intercept = 1.13

b1: Slope = 14.48

Linear Equation : Y = 1.13 + 14.48 X

If we decide to predict the value of Y when X = 7, we replace this value of X = 7 on the equation

Y = 1.13 + 14.48 (7) = 102.49

Regression Hypothesis Testing:

Ho: β1 = 0

H1: β1 ≠ 0

Decision: Reject Ho if p-value is less than α (α = 0.05)

From the Excel Data:

p-value: 0.039 (p-value for X variable 1)

0.039 < 0.05, Reject Ho

Conclusion: With a significance level of 5% (α), there is statistical evidence that the variables “X” and “Y” are related.

References:

Rajaretnam, T. (2016).  Statistics for social sciences. Sage Publications, Inc. ISBN-13: 9789351506560

Triola, M. F. (2018).  Elementary statistics (13th ed.). Pearson. ISBN-13: 978-0134462455  https://librarylogin-carolina.uagm.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=e000xww&AN=1214457&site=ehost-live&ebv=EB&ppid=pp_Cover