Please help with number 2. Thank you so much! Preview File Edit View Go Tools Wi
ID: 3155003 • Letter: P
Question
Please help with number 2. Thank you so much!
Preview File Edit View Go Tools Window Help Hw8. Spring201 6.pdf (page 2 of 2) Q Search 2. 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 the original set of 10 patients Mean St. Dev Beck score 22.1 9.15 Hamilton score 19.1 6.97 r 0.94 Copyright © 2015 Dept. of Statistics and Data Sciences, UT Austin Calculate the linear regression equation that predicts a patient's Hamilton depression score using their Beck depression score. Show all of your work and the formulas you use. (3pt) a. b. Interpret the value of the slope, in the context of the problem. (Ipt) c. Predict the Hamilton depression score for the patient who had a Beck score of 22. (lpt) d. What is the residual for the patient in part (c)? Was the prediction for this patient an overestimate or an underestimate? (lpt) 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) e. f. How much of the variation in Hamilton depression scores is explained by using the Beck scores to predict it? (Ipt)Explanation / Answer
a) Slope of regression equation, b1=r*(sy/sx), where r is correlation coefficient, sy is standard deviation of Beck score and sx is standard deviation of Hamilton score.
=0.94*(9.15/6.97)
=1.23
Intercept of regression equation, b0=ybar-b1*xbar, where ybar is mean Beck score and xbar is mean Hamilton score.
=22.1-1.23*19.1
=-1.393
yhat=-1.393+19.1x
b) With increase in 1 unit of Beck score, Hamilton score is supposed to increase by an amount of 19.1.
c) yhat=-1.393+19.1*22=418.807
f) R^2=0.8836, thus, around 88.36% variation in Hamilton score is explained by using Beck score.