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Midterm Exam ANOVA Spring 2021 Due 2/19/2020 by 11:59pm Name: Date: Approximate time to complete (Optional, please fill out for my information to help me understand how long the exam took. This...

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Midterm Exam ANOVA Spring 2021
Due 2/19/2020 by 11:59pm
Name:
Date:
Approximate time to complete (Optional, please fill out for my information to help me understand how long the exam took. This information will be used to help set the length of the final.):
Instructions: Please answer the following questions by yourself. Show all of your work. You will have one day to complete the exam.
All results needed to conduct statistical tests and estimate confidence intervals are provided. You will need to use R or other software to estimate p-values. You may use a calculator or any software of your choice for any calculations. If you choose to, you may use any software of your choice for question 2.
1. For the one-way analysis of variance model (3.3.1), p. 33, with four factor levels the 1-way ANOVA model is:
a) (10 pts)  Is estimable? Explain.
) (10 pts)  Calculate the expected value of the least squares estimator for L co
esponding to the above solution.
2. (DVD 3.14) Meat cooking experiment (L. Alvarez, M. Burke, R. Chow, S. Lopez, and C. Shirk, 1998)
An experiment was run to investigate the amount of weight lost (in grams) by ground beef hamburgers after grilling or frying, and how much the weight loss is affected by the percentage fat in the beef before cooking. The experiment involved two factors: cooking method (factor A, with two levels frying and grilling, coded 1, 2), and fat content (factor B, with three levels 10, 15, and 20%, coded 1, 2, 3). Thus there were six treatment combinations 11, 12, 13, 21, 22, 23, relabeled as treatment levels 1, 2, …, 6, respectively. Hamburger patties weighing 110 g each were prepared from meat with the required fat content. There were 30 “cooking time slots” which were randomly assigned to the treatments in such a way that each treatment was observed five times (r = 5). The patty weights after cooking are shown in Table 3.14.
(a) (5 pts) Comment on the final weight (wtloss) versus treatment scatterplot.
(b) (10 pts) Complete the analysis of variance table and test the hypothesis that color has no effect on inflation time.
Analysis of Variance Table
Response: wtloss
XXXXXXXXXXDf Sum Sq Mean Sq F value Pr(>F)
as.factor(trt XXXXXXXXXX
Residuals XXXXXXXXXX267
Total XXXXXXXXXX
SSM =
F value =
Pr(>F) =
(c) (5 pts) Comment on the residuals vs fitted plot and the normal Q-Q plot. Are you concerned that the assumptions on the model are not satisfied? If so, why? If not, why not?
(d) (5 pts) Is the analysis conducted in parts (b) and (c) satisfactory?
(e) (10 pts) Construct contrasts comparing:
a. grilled burgers to fried burgers
. 20% fat burgers to 10% fat burgers
(f) (5 pts) Estimate the contrasts in part (e) using the estimated cell means:
trt emmean SE df lower.CL upper.CL
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Confidence level used: 0.95
(g) (15 pts) Use Bonfe
oni’s method to construct a joint 95% confidence interval for the two contrasts in (f). Each color group has 5 observations (

Method Fat WtLoss
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midterm-exam-anova-spring-20211-wkjlxvcd.docx method-fat-wtloss-mkkrnbgi.docx
Answered 1 days After Feb 17, 2021

Solution

Mohd answered on Feb 18 2021
152 Votes
mid-term
mid-term
-
2/17/2021
Q1.a
An element of the boundaries of any model is supposed to be respectable if and just in the event that it very well may be composed as the normal estimation of a direct blend of the reaction factors. Just admirable elements of the boundaries have exceptional direct fair gauges. Since it looks bad to work with capacities that have an endless conceivable number of qualities, it is significant, that the investigation of the examination include just the respectable capacities.
Where bi tait and the ait's are genuine numbers. Any capacity not of this structure is non-estimable. Clearly, μ + τ1 is estimable, since it can be obtained by setting b1 1 and b2 b3 · · · bv 0. Similarly, each μ + τi is estimable. If we choose bi ci where ci 0, we see that ciτi is estimable. Any such function ciτi for which i ci 0 is called a contrast, so all contrasts are estimable in the one-way analysis of variance model. For example, setting b1 1, b2 −1, b3 · · bv 0 shows that τ1 − τ2 is estimable. Similarly, each τi − τs , i s, is estimable. Notice that there are no values of bi that give μ, τ1, τ2, . . ., or τv separately as the expected value. Therefore, these parameters are not individually estimable.
Q1.b)
li
ary(readxl)
Bloss <- read_excel("Bloss.xlsx")
summary(Bloss)
## Method Fat WtLoss
## Min. :1.0 Min. :1 Min. :71.00
## 1st Qu.:1.0 1st Qu.:1 1st Qu.:80.00
## Median :1.5 Median :2 Median :82.00
## Mean :1.5 Mean :2 Mean :81.67
## 3rd Qu.:2.0 3rd Qu.:3 3rd Qu.:84.75
## Max. :2.0 Max. :3 Max. :88.00
str(Bloss)
## ti
le [30 × 3] (S3: tbl_df/tbl/data.frame)
## $ Method: num [1:30] 1 1 1 1 1 1 1 1 1 1 ...
## $ Fat : num [1:30] 1 1 1 1 1 2 2 2 2 2 ...
## $ WtLoss: num [1:30] 81 88 85 84 84 85 80 82 80 82 ...
as.factor(Bloss$Fat)
## [1] 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3
## Levels: 1 2 3
as.factor(Bloss$Method)
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## Levels: 1 2
Fat<-as.factor(Bloss$Fat)
Method<-as.factor(Bloss$Method)
class(Fat)
## [1] "factor"
(DVD 3.14) Meat cooking experiment (L. Alvarez, M. Burke, R. Chow, S. Lopez, and C. Shirk, 1998)
An experiment was run to investigate the amount of weight lost (in grams) by ground beef hamburgers after grilling or frying, and how much the weight loss is affected by the percentage fat in the beef before cooking. The experiment involved two factors: cooking method (factor A, with two levels frying and grilling, coded 1, 2), and fat content (factor B, with three levels 10, 15, and 20%, coded 1, 2, 3). Thus there were six treatment combinations 11, 12, 13, 21, 22, 23, relabeled as treatment levels 1, 2, …, 6, respectively. Hamburger patties weighing 110 g each were prepared from meat with the required fat content. There were 30 “cooking time slots” which were randomly assigned to the treatments in such a way that each treatment was observed five times (r = 5). The patty weights after cooking are shown in Table 3.14.
Comment on the final weight (wtloss) versus treatment scatterplot.
A. In first group (frying) wtloss is decreasing with respect to increase in fat. In second group (grilling) wtloss is decreases significantly after we change fat to 20 percent.
Complete the analysis of variance table and test the effect if...
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