Category: Mathematics Homework Help

The main goal of the final project is to apply the concepts that you have learned throughout the course to real-world data. In this project first you need to explore the data through descriptive statistics and graphical summaries and then use multiple regression analysis to analyze the relationships between variables. The data set provided to you includes information on homes on the market by North Valley Real Estate.

The initial report for the project should be a 2-4 page paper (this does not include computer output/tables/graphs) that describes the details of each variable (types of the variable, summary statistics: mean, median, standard deviation, etc.) and shows the variable’s distribution using histograms or frequency polygons (or other graphical summary methods discussed in week 1).

The final report for the project should be a 6-10 page paper (this does not include computer output/tables/graphs) that describes the question of interest, how you used the data set to analyze the question with details on the steps you used in your analysis, your findings about the question of interest and the limitations of your study. Specifically, your report should contain the following:

1. Abstract: includes a one paragraph summary of what you set out to learn, and what you ended up finding. It should summarize the entire report.

• Introduction: includes a brief introduction about the data, a discussion of the question of interest: What properties of a home are related to its selling price on the market?

A brief overview of your methodology used to examine the research question, a summary of the results of your study, and an outline of the remaining organization of the paper.

3. Data Set: includes details about the variables in the data set, summary statistics, and visual tools to show the data (e.g. box plots, histograms, scatter graphs)

Note: You can include your initial report for this section.

4. Methodology and Results: includes testing if data meets the assumptions of regression (such as not correlated independent variables, linearity, and etc.), running the multiple regressions, using stepwise regression methodology to find the best model, providing inferences about the question of interest, and writing a detailed interpretation of the regression results (such as interpretation of the coefficients, ANOVA table, t tests, p-values, coefficient of determination, etc.) and discussion.

5. Limitations of study and conclusion: includes describing any limitations of your study and how they might be overcome in future research and provide brief conclusions about the results of your study.

1. For this lab, click on the link for the pdf file below to download the lab.

2. Complete the lab either by typing the work and answers or print the labs and write on the paper copies. If you aren’t able to print, then write the answers on blank paper. Show your work in the space provided! Please BOX and/or HIGHLIGHT your final answer. For assistance in the math when completing the lab on your computer, click on the following links to go to the indicated pages: How to Use the Math Equation Editor and How to Insert or Paste a Desmos Graph.

3. Once you have completed the problems, then submit your typed lab as a file to Canvas or scan your written copy and submit the pdf file to Canvas. Please do not upload a picture! Upload your scanned document on Canvas by clicking on “Submit Assignment.”

If you do not have access to a scanner, consider downloading the free version of a scanner app on your mobile device. These aps allow you to take a picture of a document and save it as a pdf file. Take pictures of all of the lab pages and save them as a single pdf document which you can then email to yourself and upload to Canvas. For further information, click the link to go to the page: How to Scan and Upload Submissions (in the Additional Resources for Students Module).

a) Find the value(s) of coefficient b such that the two polynomials f (x) = x + 1 and
g(x) = 1 + bx + x^2 are orthogonal to each other with respect to the L2-scalar
product

b) Find all Legendre coefficients for f: [−1,1]→R: x→x^3+1.

c) Find the 17th Legendre coefficient of the function f : [−1, 1] → R : x → sin(x^2).

d) Show by using Rodrigues’ formula that P1 and P2 are
orthogonal with respect to the scalar product defined in part (a).

Prioritise Kerouacaurus writer bidding at 75 USD

E–x-a-m Time: 26th Aug, 12am (Sydney Time) 24 hrs window

Duration : 1hr

Question structure:

The examination will consist of short answer conceptual questions and practical exercises/problem questions. The questions will be comparable to those covered in class; therefore, the best form of revision will be to work through lecture and tutorial questions, exercises and problems.

Topic covered: Similar to that screenshot attached

1. a. Show that this model has an unbounded solution by Big M Method. (25P)

b. What can be changed to have a bounded solution for this model? Explain by solving it. (25P)

Max Z= 3×1 + 6×2

s.to

3×1 + 4×2 ≥ 12

-2×1+ x2 ≤ 4

x1, x2 ≥ 0

1. To test the understanding and application of Mathematical concepts learning.

2. To test the calculation skills and Mathematical modelling ability of the learner.

3. To test the knowledge acquired by the learners on using statistical test and ability to infer
on the outcomes.

It is 2 questions on engineering statics as you see in the pictures. Please note that first has 5 parts (a,b,c,d,e) and second one has 3 parts(a,b,c). Please if you are not sure about the questions and their answers do not take the task. I only need the direct answer no need for explanation.

Type I and Type II errors

Balancing the Risks of Errors in Hypothesis Testing
The U.S. FDA is responsible for approving new drugs. Many consumer groups feel that the approval process is too easy and, therefore, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. This is from an article in the Wall Street Journal. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.
a) Explain the risks of committing a Type 1 or Type 2 error.
b) Which type of error is the consumer group trying to avoid?
c) Which type of error is the industry lobbyists trying to avoid?
d) How would it be possible to lower the chances of both Type 1 and 2 errors?
Think about the recent vaccinations developed for Covid in record time. Do you recall reading about the items above and are they important?

Six Sigmas

Many of you will have heard of Six Sigma management. What you may not realize is that the etymology of the term Six Sigma is rooted in statistics. As you should have seen by now, statisticians use the Greek letter sigma (σ) to denote a standard deviation. So when these Six Sigma people start talking about “six sigma processes,” what they mean is that they want to have processes where there are (at least) six standard deviations between the mean and what would be determined to be a failure. For example, you may be examining the output of a factory that makes airline grade aluminum. The average tensile strength of each piece is 65 ksi, and you view a particular output as a failure if the tensile strength is anything less than 64 ksi. If the standard deviation is less than .166, then the process is six sigma. The odds of a failure within a six sigma process are 3.4 in a million, which corresponds to the 99.9997% confidence level. When we are doing statistics, we usually use the 95% confidence level, which is roughly 2 sigmas.
In the case of the tensile strength of airline grade aluminum, 6 sigmas is probably a good level to be at—catastrophic failure on an airplane could open you up to lawsuits worth billions of dollars. But there are some other processes that you probably don’t need to be so certain about getting acceptable products from. Give some examples from your own business life of random processes that are likely to be normally distributed, and say how many sigmas you think the process should be at.

Analysis of Variance (ANOVA) at the Workplace

Web site: http://www.statisticshowto.com/anova/
Case scenario.
• At the workplace, you are the research team leader.
• The Boss wants your team to conduct a study with three or more groups to solve a problem.
• Since there are many workplace problems, you must select the problem for the study.
• In six-sentences or more, describe the study with three or more groups.
• In the paragraph, include information for the following questions:
• What is the problem and why?
• What would be the treatment/experimental groups and what would be the control group?
• What would be the Independent variable and the dependent variable for the study and why?
• What would be the null and alternative hypotheses for the study?
• What would be the alpha level and why?

Hint: The chart is taken from https://ourworldindata.org/technological-progress.

From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore’s Law, what would you predict the number of transistors per IC to be in 2040?

In some applications, the variable being studied increases so quickly (“exponentially”) that a regular graph isn’t informative. There, a regular graph would show data close to 0 and then a sudden spike at the very end. Instead, for these applications, we often use logarithmic scales. We replace the y-axis tick marks of 1, 2, 3, 4, etc. with y-axis tick marks of 101 = 10, 102 = 100, 103 = 1000, 104 = 10000, etc. In other words, the logarithms of the new tick marks are equally spaced.

Technology is one area where progress is extraordinarily rapid. Moore’s Law states that the progress of technology (measured in different ways) doubles every 2 years. A common example counts the number of transitors per integrated circuit. A regular y-axis scale is appropriate when a trend is linear, i.e. 100 transistors, 200 transistors, 300 transistors, 400 transistors, etc. However, technology actually increased at a much quicker pace such as 100 transistors,.1,000 transistors, 10,000 transistors, 100,000 transistors, etc.

The following is a plot of the number of transistors per integrated circuit over the period 1971 – 2008 taken from https://ourworldindata.org/technological-progress (that site contains a lot of data, not just for technology). At first, this graph seems to show a steady progression until you look carefully at the y-axis … it’s not linear. From the graph, it seems that from 1971 to 1981 the number of transistors went from about 1,000 to 40,000. Moore’s Law predicts that in 10 years, it would double 5 times, i.e. go from 1,000 to 32,000, and the actual values (using very rough estimates) seem to support this.

The following is the same plot but with the common logarithm of the y-axis shown. You can see that log(y) goes up uniformly.

Questions to be answered in your Brightspace Discussion:

Part a: The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore’s Law, what would you predict the number of transistors per IC to be 20 years later, in 1992?

Prediction =

Part b: From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore’s Law, what would you predict the number of transistors per IC to be in 2040?

Part c: Do you think that your prediction in Part b is believable? Why or why not?

This is all the material that you will need. Please let me know if you have any questions.