A psychiatrist wants to know whether the level of pathology (Y) in psychotic patients 6 months after treatment can be predicted with reasonable accuracy from knowledge of pretreatment symptom ratings of thinking disturbance (X1) and hostile suspiciousness (X2). The following table lists data collected on 53 patients.

a. The least-squares equation involving both independent variables is given by Ŷ = -0.0635 + 23.451X1 - 7.073X2. Using this equation, determine the predicted level of pathology for a patient with pretreatment scores of 2.80 on thinking disturbance and 7.0 on hostile suspiciousness. How does this predicted value compare with the value actually obtained for patient 5?
b. Sums of squares are shown next for three regression models. Determine the R2-values for each of these models. If you use R2 and model simplicity as selection criteria, which model appears to be the best?

Transcribed Image Text:

| 7 5 9 3 8 8 3 9 8 8 1 9 7 2 26 40888420 1 x, 9 7 7 0 1 8 0 3 8 2 570578 2223223323 3. 2 3 2 2 2 Y 0 9 3 2 3 1 0 5 9 2 1304807 tie 890123 44445555 33344 4 4 4 4 2|048473630982538987 66686857765 7. 6 6 6566 10247800035650421 16: 7 71 , 886727 7466 2. 2 3 2 3 3 2 3 3 2 2 3 3 2 2 2. 32 Y-21 22 60 10 60 2 2 3 4 8 1 7 26 26 8 1 2 90123456 2222223333333 '-. 1 0 9 0 6 3 2 9 5 8 6490062 X 6 5 6 6 7 56 7. 6 6 6 6 8 5 6 6 6 009605992 815383999 232323222332323232 704518 472645 0852552468586744 122742-24-222- ie 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 Y regressed on X Y regressed on X: Y regressed on X, and X2: SSY 13,791.1698, SSE 12,255.3128 SSE 13,633.3225 SSE = 11,037.2985