Statistics homework help
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Problem 4
a. (10) Compute AIC, BIC, and PRESSP to compare the following two models.
· The model on the first order terms for X1 and X2 and the interaction term X1X2. (model 1)
· The model on the first order terms for X1, X2 and X3 (model 2)
Do they all yield the same better model? If not, explain.
 
b. (10) Select the model that you think is better to predict the mean response value, then predict the mean response for the following case, at a confident level of 99%.
 
x1
 
x2
 
x3
 
45
 
36
 
45
Problem 5
X4 and X5 are two factors on Y.
a. (10) Is there any significant interaction effect between X4 and X5 on Y?
b. (10) With the ANOVA method, compute the 95% confidence interval for the following difference, respectively:
D1= The difference in the mean of Y when (X4=high, X5=less) and (X4=high, X5=more)
D2= The difference in the mean of Y when (X4=low, X5=less) and (X4=low, X5=more)
c. (10) With the ANOVA method, compute the 95% confidence interval for
D1-D2
Where D1 and D2 are described in b.
How is your result related to a?
 

 
1. Use these data and simple regression analysis (by Data Analysis tab in Excel) to develop linear regression models for predicting the haul cost by speed for each of these two vehicles. Discuss the strength of the models.
2. Based on the models, predict the haul cost for 35 mph and for 45 mph for each of these vehicles.
· Please submit only one Excel file for this case assignment.

Case Assignment

The following is mostly a general description of the Caterpillar company. The questions are related to regression analysis. You will do the same quick analysis in Excel

Caterpillar, Inc.

Caterpillar, Inc., headquartered in Peoria, Illinois, is an American corporation with a worldwide dealer network which sells machinery, engines, financial products and insurance. Caterpillar is the world’s leading manufacturer of construction and mining equipment, diesel and natural gas engines, industrial gas turbines and diesel-electric locomotives. Although providing financial services through its Financial Products segment, Caterpillar primarily operates through its three product segments of Construction Industries, Resource Industries, and Energy & Transportation. Some of its manufactured construction products include: mini excavators, small-wheel loaders, backhoe loaders, multi-terrain loaders, and compact-wheel loaders.

Caterpillar tractors have undertaken and completed many difficult tasks since the company’s beginning. In the 1940s, Caterpillar tractors were used in the construction of the Alaskan highway; and between 1944 and 1956, they were used to help construct 70,000 miles of highway in the United States. In the 1950s and 60s, usage of Caterpillar tractors around the world exploded and were used in such countries as Australia, Austria, Ceylon, France, Germany, Italy, Nigeria, Philippines, Rhodesia, Russia, Sweden, Switzerland, Uganda, and Venezuela, in a wide variety of projects. In addition, Caterpillar products were used to help construct the St. Lawrence Seaway between Canada and the United States. In the 1970s and 80s, Caterpillar equipment were used in numerous dam, power, and pipeline projects. Since then, Caterpillars have been used in the construction of several projects such as Japan’s Kansai International Airport as a marine airport approximately three miles offshore in Osaka Bay, the Chunnel between France and England, the “Big Dig” in Boston, Panama Canal expansion, and several Olympic Games sites.

Discussion

The United States Department of Agriculture (USDA), in conjunction with the Forest Service, publishes information to assist companies in estimating the cost of building a temporary road for such activities as a timber sale. Such roads are generally built for one or two seasons of use for limited traffic and are designed with the goal of reestablishing vegetative cover on the roadway and adjacent disturbed area within ten years after the termination of the contract, permit, or lease. The timber sale contract requires out sloping, removal of culverts and ditches, and building water bars or cross ditches after the road is no longer needed. As part of this estimation process, the company needs to estimate haul costs. The USDA publishes variable costs in dollars per cubic-yard-mile of hauling dirt according to the speed with which the vehicle can drive. Speeds are mainly determined by the road width, the sight distance, the grade, the curves and the turnouts. Thus, on a flat, straight, wide road, the speed is faster.

Shown below are data on speed and cost per cubic yard for two types of vehicles: a 12 cubic yard end-dump vehicle, and a 20 cubic yard bottom-dump vehicle.

Questions:

1. Use these data and simple regression analysis (by Data Analysis tab in Excel) to develop linear regression models for predicting the haul cost by speed for each of these two vehicles. Discuss the strength of the models.

2. Based on the models, predict the haul cost for 35 mph and for 45 mph for each of these vehicles.

 Please submit only one Excel file for this case assignment.

Due (10^th Dec, 11:45p.m).    Instructions

Question 1- Random variables

1. a) Suppose you toss a fair coin (equally likely to turn up heads or tails) four times. This procedure describes random events. What is the sample space for this procedure?

(2 points)

1. b) If we define a random variable that indicates the sum of the number of heads (in the procedure from the previous part), what is the expected value of this random variable?

(2 points)

1. c) If the coin (in the procedure from the previous part) is not fair and turns up heads a proportion p of the time (p is not 0.5), what is the expected number of heads?

(2 points)

1. d) When I lived in Toronto, in the Fall I biked home from work in the dark. My route had 4 potholes on it and I hit all four each time. I’d start my commute with my bike light turned on, but it had a loose electrical connection so each time I hit a pothole with probability p the light would switch from on to off or from off to on. What was the probability that my light would be turned on after my commute?

(2 points)

1. e) Similar to the previous part, assume that the number of potholes varied and the probability that I hit k potholes during my commute was λ^k expp´λq{k!, for a fixed λ ą This is the probability distribution function of a Poisson. This distribution arises when potholes occur independently with rate λ. Suppose that the probability that my light is switched (to off if on, to on if off) over each pothole was now p “ 1.

 
 
What was the probability that my light would be turned on after the commute, in terms of λ? (As before, my commute began with the light on). You may express your answer using trigonometric or special functions: Do not leave it as an infinite series.
(2 points)

Question 2- Multiple choice  (Show work for multiple choice questions)

1. In a study by Dr. Ryan W. Allen et al. (Environmental Pollution, 2019), air quality was assessed in 342 apartments in Ulaanbaatar, Mongolia. A total of 87 explanatory variables (‘predictor variables obtained from outdoor monitoring data, questionnaires, home assessments, and geographic data sets’; Environmental

 
Pollution, 2019) were used to predict the air quality. If p-values were computed for each of the explanatory variables, what α level would be best for assessing significance?

1. α “01
2. α “05
3. α “46E-4
4. α “75E-4
5. α “68E-6
6. Not enough information is given to provide an informed decision.
   • points)
7. On November 9th 2020, Pfizer announced interim results for a Phase 3 study on the COVID-19 vaccine BNT162b2. Their study enrolled 43,538 subjects divided into a control arm and a study arm. Their interim results indicated 90% vaccine efficacy after 94 infection events among the study subjects. What statistical tool would be most appropriate for assessing the significance of this result?
   1. An unpaired two-sample t-test.
   2. Pearson’s correlation.
   3. A log-rank test.
   4. An F-test.
   5. Fisher’s exact test.
   6. Kaplan-Meier curves.
      • points)

Research what the upcharge is for soy or almond milk for a coffee (i.e. how much more you can sell the coffee for than its dairy milk counterpart). Create two different linear models (one for soy/almond milk and one for regular milk) and, if 20% of the sales of these items were soy/almond milk, how much more money would you make vs. only selling the dairy milk version.