# Scatterplot, correlation coefficient, linear regression

See the attachments.

The regression equation and the standard error of estimate

Stewart Fleishman specializes in the psychiatric aspects of symptom management in cancer patients. Pain, depression, and fatigue can appear as single symptoms, in conjunction with one other symptom, or all together in patients with cancer. You are interested in testing a new kind of cognitive-behavioral therapy for the treatment of the simultaneous clustering of pain and fatigue in cancer patients. The following scores represent the decrease in symptom intensity (on a 10-point scale) following the new cognitive-behavioral therapy

Patient Pain (X) Fatigue (Y)

A 9 1.75

B 7 6.75

C 5 8

D 3 5.25

E 1 10

Create a scatter plot of these scores on the grid. For each of the five (X, Y) pairs, drag the orange points (square symbol) in the upper-right corner of the diagram to the appropriate location on the grid.

Calculate the means and complete the following table by calculating the deviations from the means for X and Y, the squares of the deviations, and the products of the deviations.

Scores Deviations Squared Deviations Products

X Y X-Mx Y-My (Y-Mx)^2 (Y-My)^2 (X-Mx)(Y-My)

9 1.75

7 6.75

5 8

3 5.25

1 10

Calculate the sum of the products and the sum of squares for X. SP = ______ and SSx = ______.

Find the regression line for predicting Y given X. The slope of the regression line is ______ and the Y intercept is ______.

Calculate the Pearson correlation coefficient, the predicted variability, and the unpredicted variability. The Pearson correlation is r = ______. The predicted variability is SSregression = ______. The unpredicted variability is SSresidual = ______

Calculate the standard error of the estimate. The standard error of the estimate is ______.

Suppose you want to predict the fatigue score for a new patient. The only information given is that this new patient is similar to patients A through E; therefore, your best guess for the new patient's level of fatigue is ______. The error associated with this guess (that is, the "standard" amount your guess will be away from the true value) is ______.

Suppose that now you are told the pain score for this new patient is 5.5. Now your best guess for the new patient's level of fatigue is ______. The error associated with this guess (that is, the "standard" amount your guess will be away from the true value) is ______.

Finally, suppose before estimating the regression equation, you first transform each of the original scores into a z-score. The regression equation you estimate is:

Z^y = ______ Zx

#### Solution Summary

An Excel file containing the completed table, and showing the Excel functions used in the cells, is given along with a Word file containing explanations and final answers.