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Description of Correlation and Regression Analysis.

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6. For the following scores,
X Y
3 12
6 7
3 9
5 7
3 10

a. Compute the Pearson correlation.

b. With a small sample, a single point can have a large effect on the magnitude of the correlation.
Change the score X = 5 to X= 0 and compute the Pearson correlation again. You should find that the change has a dramatic effect on the value of the correlation.

18. Sketch a graph showing the line for the equation Y= 2X + 4. On the same graph, show the line for Y = X - 4.

20. A set of n = 20 pairs of scores (X and Y values) has SSx = 25, SSy =16, and SP = 12.5. If the mean for the X values is M = 6 and the mean for the Y values is M = 4.

a. Calculate the Pearson correlation for the scores.

b. Find the regression equation for predicting Y from the X values.

22. For the following data:

a. Find the regression equation for predicting Y from X.

b. Use the regression equation to find a predicted Y for each X.

c. Find the difference between the actual Y value and the predicted Y value for each individual, square the differences, and add the squared values to obtain SSresidual.

d. Calculate the Pearson correlation for these data. Use r2 and SSY to compute SSresidual with Equation 15.18. You should obtain the same value as in part c.
X Y
1 2
4 7
3 5
2 1
5 14
3 7

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Solution Summary

The solution provides step by step method for the calculation of correlation and regression analysis. Formula for the calculation and Interpretations of the results are also included.

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C: How would you use a histogram to chart residuals? What would this tell you?

D: How do you identify outliers in your data? How do they impact your regression equation?

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