Developing A Linear Model To Make Relevant Predictions

As a researcher in the fields of biostatistics, you would like to develop a model to predict a dependent variable knowing values of the independent variable.

This project uses sample data from the textbook. The equation and associated regression data are found by using Excel.

Marks et all (A-29) conducted a study to determine the effects of rapid weight loss on contraction of the gallbladder and to evaluate the effects of ursodiol and ibuprofen on saturation, nucleation and growth, and contraction. Subjects were obese patients randomly assigned to receive ursodiol, ibuprofen, or placebo. Among the data collected were the following cholesterol saturation index values (CSI) and nucleation times (NT) in days of 13 (six male, seven female) placebo - treated subjects at the end of 6 weeks:

CSI	NT
1.20	4.00
1.42	6.00
1.18	4.00
.88	21.00
1.05	21.00
1.00	18.00
1.39	6.00
1.31	10.00
1.17	9.00
1.36	14.00
1.06	21.00
1.30	8.00
1.71	2.00

Answer in full requests a through l. Show all the computations for requests h, i, j, k.

a. Show the sample data. Describe the purpose for computing a regression model. What are

you setting out to obtain?

b. Set up a scatter diagram.

c. Assuming a linear relationship, find the simple linear regression equation.

d. Interpret the meaning of the Y intercept b_o and the slope b₁ in this problem.

e. Use the regression equation developed to make a prediction in the relevant range of the

model.

f. Determine the standard error of the estimate and interpret its meaning in this problem.

g. Determine the coefficient of determination r² and interpret its meaning in this problem.

h. Determine the coefficient of correlation r and interpret its meaning.

i. At the 0.01 level of significance, is there evidence of a linear relationship between the

dependent and the independent variable?

j. Set up a 99% confidence interval estimate for the average y variable for a point x within the

range of your model.

k. Set up a 99% prediction interval for an individual y at a point x within the range of your

model.

l. Set up a 99% confidence interval estimate of the population slope of the variables y and x.

Interpret its meaning.

A grade level A implies: a. you attach the sample data; b. you attach the scatter diagram and the summary output from excel; c. your project answers and presents all the requirements and shows all the associated computations in full; d. your project is neat; e. you submit your project on time.