# 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

 Apr 09, 2013 Regression Analysis by: Staff Answer Part I Summary of Results: 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 -------------------------------------------------------------------------------------------- Section A: Calculating the Pearson Correlation Coefficient The formula for calculating the Pearson Correlation Coefficient is: Data which will be used to calculate the Pearson Correlation Coefficient ------------------------------------------

 Apr 09, 2013 Regression Analysis by: Staff ------------------------------------------ Part II The sum of x*y values The sum of X values The sum of Y values The sum of X2 values ------------------------------------------

 Apr 09, 2013 Regression Analysis by: Staff ------------------------------------------ Part III The sum of Y2 values 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. Calculate the Pearson Correlation Coefficient. ------------------------------------------

 Apr 09, 2013 Regression Analysis by: Staff ------------------------------------------ Part IV The Pearson Correlation Coefficient for your problem data is: -------------------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------------------- Section C: Calculate the regression equation The linear regression equation has the form: ------------------------------------------

 Apr 09, 2013 Regression Analysis by: Staff ------------------------------------------ Part V The formulas for calculating linear regression coefficients "a" and "b" are shown below: Calculate regression coefficient "a" Calculate regression coefficient "b" The linear regression equation is: ------------------------------------------

 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 -------------------------------------------------------------------------------------------- Section D: Predicted Y score be if X = 99 Thanks for writing. Staff www.solving-math-problems.com