Suppose you want to use the Beck scale to predict a patient’s Hamilton scale sco

Question

Suppose you want to use the Beck scale to predict a patient’s Hamilton scale score. You confirm that all relevant assumptions were met. You have found the following summary statistics for th original set of 10 patients:

r=.94

a. Calculate the linear regression equation that predicts a patient’s Hamilton depressionscore using their Beck depression score. Show all of your work and the formulas youuse. (3pt)

b. Interpret the value of the slope, in the context of the problem. (1pt)

c. Predict the Hamilton depression score for the patient who had a Beck score of 22. (1pt)

d. What is the residual for the patient in part (c)? Was the prediction for this patient an overestimate or an underestimate? (1pt)

e. Conduct a hypothesis test to see if there is a significant linear relationship between a patient’s Beck scale score and Hamilton depression score. Include all steps for full credit. (4pt)

f. How much of the variation in Hamilton depression scores is explained by using the Beck scores to predict it? (1pt)

Explanation / Answer

Let be Beck score be x and patient's  hamilton score be y; their mean X = 22.1, Mean Y = 18.1, St dev x = 9.15 and y = 6.97, r =0.94

To predict patient's Hamiltan depression score y using Beck depression score x, we need to use, the regression line of y on x, which is given by

y - Y = r y/x ( x - X)

or y-19.1 = 0.94 * 6.97/9.15 ( x - 22.1)

y - 19.1 = 0.716(x -22.1)

y = 0.716x - 3.2764

(b) The slope of the regression line is 0.716

(c) When x = 22

   y = 0.716 * 22 - 3.2764

   = 12.4756

( d) The residual is 3.2764. It is an under estimate.

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