15. The regression equation and the standard error of estimate Aa Aa Stewart Fle

Question

15. The regression equation and the standard error of estimate Aa Aa 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 exercise therapy for the treatment of the simultaneous clustering of fatigue and depression in cancer patients. The following scores represent the decrease in symptom intensity (on a 10-point scale) following the new exercise therapy Scores Patient Fatigue (X) Depression (Y) 1.25 6.5 2.5 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. DEPRESSION 10 Scores 10 FATIGUE 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 3 1.25 4 0 5 6.5 6 2.5 7 10 -2.00 0.00 1.00 2.00 2.80 -4.05 2.45 4.00 1.00 0.00 1.00 4.00 7.84 16.40 6.00 2.40 35.40 5.60 4.05 0.00 5.95 11.90 Calculate the sum of the products and the sum of squares for X. SP = 20.00 and SSX- 10.00 . Find the regression line for predicting Y given X. The slope of the regression line is and the Y intercept is 5.95

Explanation / Answer

a) When you are estimating the new value of a a score from decrease in Depression then there are 2 ways:

1. If the coressponding value of X is provided then put the value of X in the regression eqn and find y.

2. If the value of X is not provided, then the best estimate for a new observation of Y is the mean of Y i.e. My = 4.05.

So answer to the first blank is My = 4.05.

b) The standard deviation in the observed value of Y will be the standard deviation observed in the values of Y, i.e sy = 4.12

c) By standardization of the regression equation we mean, subtracting the respective mean from X and Y and dividing by the respective S.D and then again calculating the regression equation. The resulting beta coeffecient

= b * sx/sy, where b is the older coeffecient.

So the standardised coeffecient of Zx is 5.95 * (1.58/4.12) = 2.28 approximately equal to 2.

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