STA302/1001 – Final Assignment
Due Wednesday April 22 by 11:59PM EST on Crowdmark
电子工程学Assignment代写 For each of the parts below, please provide a concise (up to three sentences) but detailed explanation for each of the concepts.
Student Name:
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Instructions: 电子工程学Assignment代写
This final assignment must be completed individually. Any sharing or discussion of questions or answers with other students will be considered an academic integrity offence. To ensure that allstudents understand the consequences of violating academic integrity, you will need to upload theattached academic integrity acknowledgment (on page 2), signed at the beginning and at the completion of this assignment. In the event of suspected integrity violations, this will serve as evidencethat a student knowingly committed an act of academic misconduct. So please ensure that you readand understand what constitutes academic misconduct as well as the consequences of so doing. 电子工程学Assignment代写
Assignments must be submitted electronically through Crowdmark. Each student will receive a personalized link to view the assignment (this is where you will submit your assignment when finished). If you do not receive this email from Crowdmark, check your spam/junk folder. In- structions for how to upload completed assignments can be found here: https://crowdmark.com/ help/completing-and-submitting-an-assignment/. Note that only PDF, PNG or JPG file types are accepted by Crowdmark. You will need to upload certain questions into certain places, so make sure you are submitting pages in the right place.
The assignment is divided into five questions.
Each question needs to be uploaded under the correct section in Crowdmark, otherwise it may be overlooked when graded. For questions that require hand calculations or proofs/derivations, you must show all your work. You may submit handwrittenanswers for these question, but they must be legible and neat. For questions involving R, you must provide an appendix that contains all the R code used to complete the question. We need to be able to verify that your answers can actually be produced from your code. Please do not have R code or unnecessary R output in your solutions. This should be in the appendix. 电子工程学Assignment代写
Note that as this is meant to replace a final exam and we are keeping the due date of the original final exam, this means that NO EXTENSIONS WILL BE GRANTED. Therefore, if you have not submitted by April 22 at 11:59PM EST, you will receive a grade of zero. To ensure that you submit on time, please start the submission process early, especially if you have unreliable internet access.
Academic Integrity Acknowledgement Form
Academic integrity is a fundamental value of learning and scholarship at the UofT. Participatinghonestly, respectfully, responsibly, and fairly in this academic community ensures that your UofTdegree is valued and respected as a true signifier of your individual academic achievement.
Prior to beginning this final assignment, you must attest that you will follow the Code of Behaviouron Academic Matters and will not commit academic misconduct in the completion of this assess- ment. Affirm your agreement to this by completing the following Statement: 电子工程学Assignment代写
By signing this Statement, I, , agree to fully abide to the Code of Behaviour on Academic Matters. I will not commit academic misconduct and am aware of the penalties that may be imposed if I commit an aca- demic offence.
The University of Toronto’s Code of Behaviour on Academic Matters outlines the behaviours that constitute academic misconduct, the processes for addressing academic offences, and the penalties that may be imposed. You are expected to be familiar with the contents of this document.
Potential offences include, but are not limited to:
- Using someone elses ideas or words without appropriate acknowledgement (this includesfrom internet sources or textbooks).
- Submittingyour own work in more than one course without the permission of the instructor.
- Making up sources or facts. 电子工程学Assignment代写
- Obtainingor providing unauthorized assistance on any assignment (this includes working in groups on assignments that are supposed to be individual work).
- Looking at someone else’s answers, or working together to answer questions.
- Lettingsomeone else look at your answers.
- Misrepresenting your identity or having someone else complete your test or exam.
All suspected cases of academic dishonesty will be investigated following the procedures outlined in the Code of Behaviour on Academic Matters.
Please sign the Statement below to complete your assessment.
By signing this Statement, I, , am attesting to the fact that I have abided fully to the Code of Behaviour on Academic Matters. I have not committed academic misconduct, and am aware of the penalties that may be imposed if I have committed an academic offence.
Question 1 (12 points) – This question must be done by hand (but may be typed for submission) 电子工程学Assignment代写
Consider a study design in which we have collected multiple response measurements at each value of the predictor. Suppose we have ni observed responses at each value of xi, indexed by i = 1, . . . , m, and yij corresponds to the j-th observation on the response, j = 1, . . . , ni for the i-th value of the predictor. This means we have m unique predictor values, and ni response measurements for each of the m values of the predictor. In this situation, it is possible to create a test that can be used to test for how poorly the regression line captures the linear relationship.
(a)(4 points) Consider the traditional variance decomposition of a simple regression model: SST = SSReg + RSS. Show that we can further decompose the residual sum of squares into
- thepure error (i.e. deviations of the individual responses from the average response at each unique value of the predictor), denoted by SSP ure
- andthe lack of fit error (i.e. deviations of the average response at each x value from the regression line), denoted by SSLack.
(b)(1 points) Determine the degrees of freedom for the pure error and the lack of fit
(c)(3points) Determine the expected values of the mean squares of the pure error (MSPure) and the lack of fit error (MSLack). You may assume that model assumptions are
(d)(2points) The test statistic for this test is
Explain why this should follow an F distribution.
(e)(2points) Based on the test statistic in (d) and the expected values in (c), explain why a largevalue of the test statistic implies that the true regression function is not linear, and thus the fit of our regression model is poor.
Question 2 (15 points) – This question must be done by hand (but may be typed for submission) 电子工程学Assignment代写
A study was run to compare the effect of three different drugs on reducing the pain caused by a particular condition. The drugs are labelled A, B, and C, and the response of interest is a pain scale rating (integer-valued), where higher values implies more pain. The goal of the study was to determine whether there exists a difference in the average pain rating between the three drug treatments. We can answer this question using multiple linear regression methods. The data can be found below:
| Drug | A | 4 | 5 | 4 | 3 | 2 | 4 | 3 | 4 | 4 |
| Drug | B | 6 | 8 | 4 | 5 | 4 | 6 | 5 | 8 | 6 |
| Drug | C | 6 | 7 | 6 | 6 | 7 | 5 | 6 | 5 | 5 |
(a)(2points) Show that we can represent the three treatments/drugs in the form of two indicator variables. Why don’t we require the use of a third indicator variable?
(b)(2points) Find the XjX and XjY matrices for these data. 电子工程学Assignment代写
(c)(3points) Estimate the regression coefficients for a multiple linear regression model relating the pain response Y to the three drugs, X.
(3points) Show that the above regression model can be re-expressed as
yij = µ + τi + sij
where µ is the overall average pain rating, τi is the average pain rating for drug i, sij is the random error in the pain rating for individual j and drug i, and yij is the pain rating for individual j on drug i.
(e)(5 points) Perform an appropriate hypothesis test using your model from (c) to determine whether the average pain ratings for each drug are equal (i.e. τi= 0 for all i). Use a significance level α = 0.05 and the residual standard error of 1.089.
Question 3 (8 points) – This question must be done by hand (but may be typed for submission)
For each of the parts below, please provide a concise (up to three sentences) but detailed explanation for each of the concepts. Make sure you use your own words for your answers. 电子工程学Assignment代写
(a)(2points) Suppose we have the following correlations between a response variable and twopredictor Explain which predictor the forward selection method would add to the model first. Would the method then add the second predictor variable? Why or why not?
| Y | X1 | X2 | |
| Y | 1 | 0.93 | -0.99 |
| X1 | 0.93 | 1 | 0.985 |
| X2 | -0.99 | 0.985 | 1 |
(b)(2points) Explain how violations in the model assumptions affect the ANOVA test of overall significance in simple linear regression.
(c)(2points) In the event that condition 1 or 2 fails, explain why we are unable to use the specificpatterns seen in the residual plots to tell us in what way the model assumptions are violated.
(d)(2points) Explain why, when you have response measurements that are means or medians,using a weight equal to the number of observations used to create that value can correct for violations of constant variance. 电子工程学Assignment代写
Question 4 (10 points) – This question must be completed using R 电子工程学Assignment代写
Consider the New York City menu dataset, which can be found on the assignment page on Quercus or attached with this question.
(a)(1 points) Fit a multiple linear regression model to predict Price from the variables Food, Decor, and East. Extract the residuals from this model and save What do they representin the context of this model?
(b)(1points) Fit a multiple linear model to predict Service from Decor, Food and Extract the residuals from this model and save them. What do they represent in the context of this model?
(c)(1points) What can we say about the predictors based on the model from (b)?
(d)(2 points) Plot the residuals saved from part (a) against the residuals saved from part (b). Add a line representing the simple linear regression relationship between these two setsof residuals. What relationship do you see between the two sets of residuals? 电子工程学Assignment代写
(e)(3points) Compare the relationship in your plot from (d) to a multiple linear model predicting Price from the variables Food, Decor, Service and What similarities do you see? What does the plot represent and how does it achieve this?
(f)(2points) How else might this plot be used for diagnostic purposes?
Question 5 (20 points) – This question must be completed using R 电子工程学Assignment代写
For this question, you will be using the housing.proper.csv dataset which can be found on the assignment page on Quercus or attached to this question on Crowdmark. These data consist of the median value of owner-occupied homes (Y ) in suburbs of Boston, along with a number of different neighbourhood characteristics. It contains 506 observations on 13 covariates. You are asked by a real estate developer to build the best possible model to predict the median value of homes in a new subdivision being built, but that is also interpretable so they can justify the use of this model to shareholders.
The possible predictors for this model include:
- X1= per capita crime rate by town
- X2= proportion of residential land zoned for lots over 25000 square
- X3= proportion of non-retail business acres per town
- X4= Charles River indicator variable (1 = near river, 0 = far from river)
- X5= nitric oxide concentration (parts per 10 million)
- X6= average number of rooms per dwelling
- X7= proportion of owner occupied units built prior to 1940
- X8= weighted distance to five Boston employment centres
- X9= index of accessibility to radial highways
- X10= full-value property-tax rate
- X11= pupil-teacher ratio by town
- X12= 1000(B − 0.63)2, where B is the proportion of African Americans by town
- X13= a numeric vector of percentage values of lower status population
You may use any technique shown in class to arrive at your final model, but you must justify everydecision you make.
You will be asked to interpret your final model, explain how you arrived at this model and defend why you think this is the best possible model. You may use up to 5 plots inyour explanations and each plot must have a reason for being presented. 电子工程学Assignment代写
Please do not include toomuch R output (ideally fewer than 5 outputs) as all your decisions and model diagnostics shouldbe discussed in the text rather than presented with R output. The discussion of your model should be no longer than 500 words. All R code should be at the end in an appendix so we can verify your final model and the steps you took to arrive there. Your report with plots and output should reasonably be no longer than 3 pages, with the appendix attached after. Do not overload your appendix with code or output that is not relevant to the creation of your final model.
Rubric for question 5 电子工程学Assignment代写
| Characteristic | Insufficient (1 point) |
Adequate (3 points) |
Excellent (5 points) |
|
Presentation: Is the report easy to follow, and are graph- ical/output components used correctly? |
Justification is far too
long or is missing a number of key deci- sions, may have seri- ous grammatical errors and/or logic of analy- sis is difficult to follow; plots are not at all ref- erenced and/or do not support the decisions or discussion of model |
Justification is a bit
long-winded and/or is missing a few key steps, may have some grammar errors and/or logic of analy- sis a bit hard to follow; some plots are not referenced and/or are not quite helpful for the discussion |
Justification is concise yet thorough, gram- matically correct and easy to follow; plots presented are refer- enced and valuable to the report, and a clear picture of the analysis is given. |
|
Model Build- ing: Were vari- ables chosen in a reasonable way? |
No or minimal statisti- cal methods were used to select variables in the model and/or were used incorrectly and/or jus- tification for choices not given, or not stated |
Only statistical rea-soning has been used to select variables without reference to context; methods em- ployed have been used correctly, justification for methods may be lacking |
Both statistical and contextual reasoning has been used to determine variables included in model, and have been used cor- rectly with sufficient justification |
|
Model Diag- nostics: Does the model have the correct properties? |
None or a minimal
amount of diagnostics were made on the final model, and/or no men- tion of appropriateness of model provided, and/or no corrections made/justifications given |
Some diagnostics have been performed but some are missing, and/or if problems were detected, lit- tle/no justification was given for how they were handled | All diagnostics have been performed and model violations have been documented; any other problems with the model have been dealt with and justified appropriately |
|
Final Model: Is the model meaningful and useful? |
Model is overly com-plicated which makes interpretation difficult and/or interpretation of model is incorrect or model is too simplistic and important predic- tors are missing and/or model not validated and/or limitations of model not stated |
Model has too
many/too few pre- dictors, although relationship to re- sponse still reasonable and interpretable, and/or interpretation has some flaws, model has been validated but limitations of model not reported. |
Model shows reason- able relationship to re- sponse, is easily in- terpretable, and has been interpreted cor- rectly and validated, and further limitations of model documented. |
