Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
A sample midterm exam for the isye6413 course focusing on statistical analysis and experimental design. The exam includes five problems covering topics such as model adequacy, anova, multiple regression, and experimental design. Students are expected to apply statistical concepts and methods to analyze data and draw conclusions.
Typology: Exams
1 / 5
This page cannot be seen from the preview
Don't miss anything!
Problem 1 2 3 4 5 Total Max Points 4 6 6 12 12 40 Your score
Problem 1 (4 pts) If the plot of residuals against the fitted values exhibits a reverse funnel shape, i.e., the spread of residuals is larger for smaller fitted values and vice versa. What does it suggest you regarding model inadequacy?
Problem 2 (6 pts) Consider a two-way layout with the model yi j = η + αi + β (^) j + εi j, and i = 1 , 2 , 3 and j = 1 , 2, where αi and β (^) j represent the main effects of two qualitative factors. Suppose it is determined that α 3 = 0 and β 2 = 0 be chosen as the baseline constraints. Find estimates of α 1 , α 2 , and β 1 in terms of the yi j values.
Problem 4 (12 pts) The bioactivity of four different drugs A, B, C, D for treating a particular illness was compared in a study and the following ANOVA table was given for the data:
Source Sum of squares Degrees of freedom Between treatments 64.42 3 Within treatments 64.12 26 Total 128. 54 29
(a) (3 pts) Describe a proper design of the experiment to allow valid inferences to be made from the data.
(b) (3 pts) Use an F test to test at 0.05 level the null hypothesis that the four treatments have the same bioactivity. Compute the p value of the observed F statistic. (Hint: interpolate between values in different F tables.)
(c) (3 pts) The treatment averages are as follows: ¯yA = 66 .10 (7 samples), ¯yB = 65 .75 (8 sam- ples), ¯yC = 62 .63 (9 samples), ¯yD = 63 .85 (6 samples). Use the Tukey method to perform multiple comparisons of the four treatments at the 0.05 level.
(d) (3 pts) It turns out that A and B are brand-name drugs and C and D are generic drugs. To compare brand-name vs. generic drugs, the contrast 12 ( y¯A + y¯B) − 12 ( y¯C + y¯D) is computed. Obtain the p-value of the computed contrast and test its significance at the 0.05 level. Com- ment on the difference between brand-name and generic drugs.
Problem 5 (12 pts) The data considered in this problem are taken from 20 incoming shipments of chemicals in drums arriving at a warehouse. The response Y is the number of minutes required to handle a shipment. There are two predictors:
(i) X 1 : number of drums in the shipment.
(ii) X 2 : total weight of the shipment (hundreds of pounds).
After running a multiple regression code in a standard statistical software, the following results are obtained:
Predictor Coef SE Coef T Constant 3.324 3.111 1. X1 3.7681 0.6142 6. X2 5.0796 0.
(a) (2 pt) Compute the t-value corresponding to X 2.
(b) (3 pts) Test whether the predictor variables X 1 and X 2 significantly affect Y at level 0.01.
(c) (4 pts) Estimate the average value of Y at X 1 = 5 and X 2 = 16 .00. Find the 95% confi- dence interval for the estimated average. The (X′X)−^1 matrix is given below to aid your calculation:
(d) (3 pts) Obtain the 95% prediction interval for a single future observation Y corresponding to X 1 = 5 and X 2 = 16 .00.
