Question

The accompanying table presents the correlation coefficients between weight (x1), age (x2), and total cholesterol (y), separately, for a sample of 60 patients with hyperlipoproteinemia (disorder related to high cholesterol) before being subject to drug therapy. weight (x1) age (x2) chol (y mean SD weight (x1) .42 .67 68.68 12.72 age (x2) 84 39.12 12.24 chol (y) ------ 310.72 77.82 Step Variable entered R 0 R2 SE Partial r's | 77.82 | 76.21 .83 73.56 2 1.91 a. In a stepwise multiple regression, what variable would be entered at step 1, and why? (2) b. The partial r for the remaining variable is .64 and is significant. Explain to me what this means. Would you proceed with Step 27 (3) c. The multiple R and R2 at step 2 have been provided to you. Explain what each these values are telling us. (4) d. Why are the SE values decreasing at each step? (3)

Answer 1

ANSWER:-
(a) the variable with maximum correlation with y Chol) will be entered first because it will be able to explain maximum variability possible in yiey x2 will be entered first as it as 6184 correlation. (6) this means that xl has correlation with y in presence of x2=0.67 and in absense of x2 or the correlation of X1 alone with y is 0164 which means that the variables X, and X2 are negligibly correlated and explain different Variabilities in Ÿ and both are important and significant In Step 2, We will include X1 also in the model Ris the multiple correlation of it with 41 and 42=0.91 (strong and positive) lie, as xl and x2. increase, y increases. R-sq = 0183 be , XA and tz together explain 83% Vadiability in y (chol) (d) The SE or standard error is the residual or unexplained Variation remains in y. that

Since; we are adding significant variables at each Step that are explaining some part of vasiability in Y and hence, unexplained variability reduces at each Step. Therefore, SE reduces at each step.