STA302/1001 - Assignment # 4Due Friday April 10 by 11:59PM on CrowdmarkStudent 1 Name:Student 1 Email:Student 2 Name:Student 2 Email:Instructions:Assignments must be submitted electronically through Crowdmark. Each student will receive apersonalized link to view the assignment (this is where you will submit your assignment whenfinished). If you do not receive this email from Crowdmark, check your spam/junk folder. Instructionsfor how to upload completed assignments can be found here: https://crowdmark.com/help/completing-and-submitting-an-assignment/. Note that only PDF, PNG or JPGfile types are accepted by Crowdmark. You will need to upload certain questions into certainplaces, so make sure you are submitting pages in the right place.Students may work in groups of no more than 2 people, with only one assignment submitted toCrowdmark per group. When you receive your personalized link to the assignment, you may thenenter your group members name. A shared submission link will be sent to both group members, soyou can both submit the assignment or edit submissions. Only one assignment should be submittedper group.The assignment is divided into four questions, each with subparts. Each question needs to be uploadedunder the correct section in Crowdmark, otherwise it may be overlooked when graded. Onequestion is a calculation-type question, one will be a theoretical/derivation/proof type question, andone will involve using R. You should make sure to show all your work with the first two questions,while the R questions should be presented in a report-type format (i.e. include output and graphswith written explanations of answers in the main document, R code places in an appendix at theend). If you are comfortable with RMarkdown, it is recommended to complete your assignmentwith it. Otherwise, any word processing document will suffice for the R question. You may submithandwritten answers for questions 1 and 2, but they must be legible and neat.Note that there is a 20% per day late penalty on assignments. After 48 hours of being late, theassignment will no longer be accepted. This means that you should submit your assignment nolater than Sunday April 12 at 11:59PM to avoid receiving a grade of zero.1Question 1 (14 points) - Derivations/Proof QuestionThis question walks you through how to prove the equivalence of two of the formulae for theCook’s Distance using matrix notation. Suppose X(i)is the (n − 1) × (p + 1) design matrix withobservation i removed, and X is the n × (p + 1) design matrix with all observations. Let xi bea column vector representing the predictor values for observation i, and yiis the response value(scalar) for observation i. Finally, βˆ is the column vector of predictors estimated using the full data,and βˆ(i)is the column vector of predictors estimated without using observation i.(a) (2 points) Show how we would predict the response for observation i using the regressionmodel that has been fit without observation i.(b) (3 points) Using the fact that βˆ = (X0XSTA302/1001作业代做、代写R课程设计作业、代做data作业、代做R编程语言作业 帮做Java程序|代写Data)−1X0Y, and the following result,show that post-multiplication of this result by (X0Y − xiyi) yieldsβˆ(i) = βˆ − (X0X)−1xiyi +(X0X)−1xix.(d) (4 points) Using your result in (c), Question 2 (16 points) - Hand Calculation QuestionWe previously considered building multiple linear regression models for gas mileage of cars basedon characteristics of each vehicle model. We can now consider a few different models and attemptto determine which model is better.(a) (4 points) Using the table of summary values below, and that we have taken a sample of 30vehicles, compute the AIC for each of the three models. Based on these values, which modelwould you say is better?Model Predictors Residual Standard ErrorModel 1 all 11 predictors 3.227Model 2 Displacement, Horsepower, Torque, Number ofTransmission Speeds, Weight 3.245Model 3 Displacement, Horsepower, Weight 3.171(b) (4 points) Using the above summary table, calculate the corrected AIC for each of the abovemodels. Based on this, would we prefer the same model as in part (a)?(c) (4 points) Now, knowing that the sample variance of gas mileage is 39.28 MPG, find theadjusted coefficient of determination for each of the models in (a). Based on this measure,which model is preferred?(d) (4 points) Suppose we consider the smallest model (model 3 from part (a)). We can fit amodel using each predictor as a response using the remaining predictors as predictors. Belowis a summary of each of these models.Response Predictors Residual SE Sample Variance of ResponseDisplacement Horsepower, Weight 27.21 13511.05Horsepower Displacement, Weight 15.64 1993.689Weight Displacement, Horsepower 299.1 885420.2Find the Variance Inflation Factor of each predictor. Should we be concerned about multicollinearityin the model 3 from (a)?3Question 3 (14 points) - R Data Analysis QuestionUse the dataset found on Quercus under Assignment 4 materials to answer the below questions.These data contain information on 50 men, on which were measured their percent body fat, theirheight, their waist size, and their chest size.(a) (1 points) Fit a multiple linear model to predict Percent Body Fat (Pct.BF) from waist size,height and chest size.(b) (3 points) Determine whether there are any:(a) leverage points(b) outlier observations(c) influential observations. If there are, in what way do they influence the regression surface?(c) (3 points) Can we use our residual plots to make conclusions regarding which assumptionsare violated? Support your answer using appropriate plots.(d) (3 points) Determine whether the model from (a) is a valid model using appropriate plots.(e) (2 points) Determine whether there is multicollinearity among the predictor variables.(f) (2 points) Create an indicator variable for each of the observations 19 and 38. Add theseindicator variables to the model in (a) as main effect terms. Show that we have now removedthe influence of these observations from the model by showing that they no longer appear asinfluential observations.4转自：http://www.daixie0.com/contents/18/4919.html