Intermediate Biostatistics: Regression and Correlation - Week 3 Practice Problems, Exams of Community Health

Download Intermediate Biostatistics: Regression and Correlation - Week 3 Practice Problems and more Exams Community Health in PDF only on Docsity! PubHlth 640 Intermediate Biostatistics 1 Unit 2 – Regression and Correlation Practice Problems - Week #3 Due: Monday February 23, 2009 1. A psychiatrist wants to know whether the level of pathology (Y) in psychotic patients 6 months after treatment could be predicted with reasonable accuracy from knowledge of pretreatment symptom ratings of thinking disturbance (X1) and hostile suspiciousness (X2). (a) The least squares estimation equation involving both independent variables is given by Y = -0.628 + 23.639(X1) – 7.147(X2) Using this equation, determine the predicted level of pathology (Y) for a patient with pretreatment scores of 2.80 on thinking disturbance and 7.0 on hostile suspiciousness. How does the predicted value obtained compare with the actual value of 25 observed for this patient? (b) Using the analysis of variance tables below, carry out the overall regression F tests for models containing both X1 and X2, X1 alone, and X2 alone. Source DF SSQ Regression on X1 1 1546 Residual 51 12246 Source DF SSQ Regression on X2 1 160 Residual 51 13632 Wk3_practice.doc corrected 2-22-2009 PubHlth 640 Intermediate Biostatistics 2 Source DF SSQ Regression on X1 , X2 2 2784 Residual 50 11008 (c) Based on your results in part (b), how would you rate the importance of the two variables in predicting Y? (d) What are the R2 values for the three regressions referred to in part (b)? (e) What is the best model involving either one or both of the two independent variables? #2. In an experiment to describe the toxic action of a certain chemical on silkworm larvae, the relationship of log10(dose) and log10(larva weight) to log10(survival) was sought. The data, obtained by feeding each larva a precisely measured dose of the chemical in an aqueous solution and then recording the survival time (ie time until death) are given in the table. Also given are relevant computer results and the analysis of variance table. Larva 1 2 3 4 5 6 7 8 Y = log10(survival time) 2.836 2.966 2.687 2.679 2.827 2.442 2.421 2.602 X1=log10(dose) 0.150 0.214 0.487 0.509 0.570 0.593 0.640 0.781 X2=log10(weight) 0.425 0.439 0.301 0.325 0.371 0.093 0.140 0.406 Larva 9 10 11 12 13 14 15 Y = log10(survival time) 2.556 2.441 2.420 2.439 2.385 2.452 2.351 X1=log10(dose) 0.739 0.832 0.865 0.904 0.942 1.090 1.194 X2=log10(weight) 0.364 0.156 0.247 0.278 0.141 0.289 0.193 Y = 2.952 – 0.550 (X1) Y = 2.187 + 1.370 (X2) Y = 2.593 – 0.381 (X1) + ).871 (X2) Source DF SSQ Regression on X1 1 0.3633 Residual 13 0.1480 Wk3_practice.doc corrected 2-22-2009