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Statistics - Pearson correlation











































Regression Equation

For the data below, compute the Pearson correlation. Is it significant? Also, calculate
a regression equation. What would my predicted Y score be if I scored 99 on X?

X       Y
30     40
20     50
10     99
60     20

Comments for Statistics - Pearson correlation

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Apr 09, 2013
Regression Analysis
by: Staff


Answer


Part I


Summary of Results:

Graph of Regression Equation





The answer is divided into four sections:

Section A: Calculating the Pearson Correlation Coefficient

Section B: The significance of the Pearson Correlation Coefficient

Section C: Calculate the regression equation

Section D: Predicted Y score be if X = 99

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Section A: Calculating the Pearson Correlation Coefficient


The formula for calculating the Pearson Correlation Coefficient is:

The formula for calculating the Pearson Correlation Coefficient





Data which will be used to calculate the Pearson Correlation Coefficient

The data  for calculating the Pearson Correlation Coefficient





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Apr 09, 2013
Regression Analysis
by: Staff


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Part II


The sum of x*y values

The sum of x*y values to be used in the calculation of the Pearson Correlation Coefficient





The sum of X values

The sum of x values to be used in the calculation of the Pearson Correlation Coefficient





The sum of Y values

The sum of y values to be used in the calculation of the Pearson Correlation Coefficient




The sum of X2 values

The sum of x squared  values to be used in the calculation of the Pearson Correlation Coefficient





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Apr 09, 2013
Regression Analysis
by: Staff


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Part III


The sum of Y2 values

The sum of y squared  values to be used in the calculation of the Pearson Correlation Coefficient





Substitute the numerical sum of X*Y values, the sum of X values, the sum of Y values, the sum of X2 values, the sum of Y2 values, and 4 for "n" into the formula for calculating the Pearson Correlation Coefficient.

Substitute the numerical values for  ∑XY, ∑X, ∑Y, ∑X², ∑Y², and 4 for n into the formula for the Pearson Correlation Coefficient





Calculate the Pearson Correlation Coefficient.

Calculate the Pearson Correlation Coefficient.






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Apr 09, 2013
Regression Analysis
by: Staff


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Part IV


The Pearson Correlation Coefficient for your problem data is:

Pearson Correlation Coefficient - final answer.





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Section B: The significance of the Pearson Correlation Coefficient

The following estimates have been reproduced from:

http://faculty.quinnipiac.edu/libarts/polsci/Statistics.html

If r = +.70 or higher Very strong positive relationship

+.40 to +.69 Strong positive relationship

+.30 to +.39 Moderate positive relationship

+.20 to +.29 weak positive relationship

+.01 to +.19 No or negligible relationship

-.01 to -.19 No or negligible relationship

-.20 to -.29 weak negative relationship

-.30 to -.39 Moderate negative relationship

-.40 to -.69 Strong negative relationship

-.70 or higher Very strong negative relationship


A Pearson Correlation Coefficient of -.86415 shows a very strong negative relationship.


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Section C: Calculate the regression equation


The linear regression equation has the form:

A linear regression equation has the form y = a + bx.






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Apr 09, 2013
Regression Analysis
by: Staff


------------------------------------------


Part V


The formulas for calculating linear regression coefficients "a" and "b" are shown below:

Formulas for calculating the linear regression coefficients 'a' and 'b'





Calculate regression coefficient "a"

Calculating the linear regression coefficient 'a'





Calculate regression coefficient "b"

Calculating the linear regression coefficient 'b'





The linear regression equation is:

Linear regression equation y = 92.5 - 1.3x






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Apr 09, 2013
Regression Analysis
by: Staff


------------------------------------------


Part VI


For your information, you can also use Excel to calculate the Pearson Correlation Coefficient.

Click the following link to VIEW the instructions.

Calculate the Pearson Correlation Coefficient and Regression Coefficients using Excel



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Section D: Predicted Y score be if X = 99

Predicted Y score be if X = 99









Thanks for writing.

Staff
www.solving-math-problems.com



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