# Homework 05 BIOS 517D/Biostats

Homework 05 BIOS 517D/Biostats

1. What are the four linear regression assumptions Explain each assumption in at most two sentences; use plain English. 2. Read the bodyfat data set into SAS. The

relationship of interest is between body fat percentage (as measured using Siri���s formula) and abdominal girth (cm). The model is BODYFATi = ��0 + ��1(ABDOMENi ���90) + ��i

(a) Draw a scatterplot showing the relationship between abdominal girth and body fat. Show 95% con���dence and prediction bands. Does the plot suggest a linear

relationship between the variables Explain brie���y. (b) When you run proc reg for the model above, SAS obtains estimates of three pa- rameters: ��0, ��1 and ��2. Fill in

the table below.
Model Point Concise Parameter Estimate Interpretation
��0
��1
��
(c) Construct the residual plot and the normal probability plot for residuals (similar to Figure 15.7 on p. 675). What do these plots suggest (d) Report and interpret

the coef���cient of determination. (e) If you take a different sample of n = 252 male adults from the same population with the same abdominal girth values, are you

likely to obtain the same estimates of ��0, ��1 and ��2 (You���d better answer ���No.���) Because the estimates of these pa- rameters change from sample to sample, we say that

each of the estimates has a sampling distribution. i. What is an estimate of the standard deviation of the sampling distribution of b ��0 In other words, ���nd the

standard error of the statistic. ii. What is an estimate of the standard deviation of the sampling distribution of b ��1
(f) In the proc reg output below, ���nd the t-value for ABDOMEN. Hint: Use the formula t = (b ��1 �����1)/SE(b ��1). Parameter Standard Variable DF Estimate Error t Value Pr

> |t| Abdomen 1 0.63130 0.02855 <.0001 i. usingtheformula t that for large n is close to check your answer using the clb option in proc reg. ii. doesthe95 cally signi linear relationship between body fat percentage and abdomi- nal girth explain brie a researcher interested testing null hypothesis population corre- lation coef zero. what value of sample correlation do you have reason believe differ- ent from zero test statistic p-value are going report explain. example textbook. obtain con interval id has an abdominal cm this subject residual interpret value. predict adult male with cm. note: there no data set whose reporta95 interval. iii. prediction individual iv. which two intervals wider did expect result reporta99 brozek siri density age weight height adiposity free neck chest abdomen hip thigh knee ankle biceps forearm wrist>