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Project B: Correlation and Linear Regression     PART I: CALCULATION AND ANALYSIS 1) Name your source and include the link to where the data was found

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Project B: Correlation and Linear Regression

 

 

PART I: CALCULATION AND ANALYSIS

1) Name your source and include the link to where the data was found.  Give your data set in an organized, presentable fashion.

 

2. Explain the variables and what the units mean. 

 

 

3. Explain the reasoning for why one variable is independent, and the other variable is dependent.

 

 

 

4. Choose α and explain why you chose it.

 

 

5.  Give your p-value.

 

6. Compare α and p-value

 

7. Tell if there is positive, negative or no significant correlation.

 

8. Give the bottom-line conclusion; does the “y” depend on the “x”?

 

9. Give the critical value and r.

 

 

10. Compare r and critical value and tell if there is significant correlation.

 

11. Give r² and explain what it means, using the specific variables of the project.

 

12.  Give other causes of variation that are not part of the model.

 

 

 

 

13. Give the regression equation.

 

14. Explain what the slope ( ΔyΔx

 ) means in the model (for your specific x and y) and give the units.

 

 

15. Pick 3 data points that will be used to find their residuals.  Give the names of the data points, why they were chosen, and why they are important.

 

16. Find the residuals for the 3 points chosen in #16.

 

 

17. Decide if the residuals are small or large and explain why.  Large is defined as the absolute value of the residual being more than 30% of the value of the y it is associated with.  For example, if the residual is -6.2, and the associated y value is 4, then the residual is (|-6.2| - 4)/4 *100 = 55%, which is greater than 30%, so the residual is considered large.

 

 

 

 

 

 

 

18. Make one prediction.  For a time, series, predict the next year.  Otherwise, make a prediction about a fictional data point that is realistic and relevant to business, or, if available, a real data point that is not part of the data set.  If all the available data points were used in the data set (for example, if the data is states, and all 50 states were used in the data set), the fictional data point should be interesting, such as being very large, very small, equal to the average, or having any other characteristic the author feels makes it interesting.

 

 

 

 

 

PART II: CRITICAL THINKING AND APPLYING TO THE REAL WORLD

 

 

20. Why did you pick this topic and how is it important to you?

 

 

 

21. How can this model be of use to a real-world business?  Can it help solve any problems?

 

 

22. Explain what Type I Error would be for this model and how Type I Error can be dangerous to a business using this model.  How concerned are you about this and why? Before you answer this question, look up Type I Error and reflect on what it means, because Type I Error is subtle.

 

 

23. Correlation and causality

 

 

24. Time dependent correlation and causality

 

 

25. Randumbness

 

 

26. Regression to the moon

 

 

 

27. False linear assumption (Study the scatter plot and determine if the data might actually not be linear, and if so, what other type of correlation it might be.)

 

 

28. What did you learn about this topic? Write at least 4 sentences.

 

 

 

 

29. What did you learn about statistics? Write at least 4 sentences.