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. .42 chol(y) weight (x1) age (x2) chol (y) mean SD weight (x1) .67 68.68 12.72 age (x2) .84 39.12 12.24 310.72 77.82 Step Variable entered R R2 SE Partial r's 0 77.82 76.21 2 1.91 .83 73.56 1 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 22 (3) c. The multiple R and R2 at step 2 have been provided to you. Explain what each of these values are telling us. (4) d. Why are the SE values decreasing at each step? (3)

Answer 1

a. The variable with maximum correlation with y (chol) will be entered first because it will be able to explain maximum variability possible in y i.e., X2 will be entered first as it as 0.84 correlation

b. This means that X1 has correlation with y in presence of X2 = 0.67 and in absense of X2 or the correlation of X1 alone with y is 0.64 which means that the variables X1 and X2 are negligibly correlated and explain different variabilities in y and both are important and significant. In step 2, we will include X1 also in the model

c. R is the multiple correlation of y with X1 and X2 = 0.91 (strong and positive) i.e., as X1 and X2 increase, y increases.

R-sq = 0.83 ie., X1 and X2 together explain 83% variabillity in y(chol)

d. The SE or standard error is the residual or unexplained variation that remains in y.

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

Therefore, SE reduces at each step

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