# Assignment: linear statistics problems

Assignment: linear statistics problems ORDER NOW FOR CUSTOMIZED AND ORIGINAL ESSAY PAPERS ON Assignment: linear statistics problems Help me study for my Statistics class. Im stuck and dont understand. The below document is the problem sets. Please help me with problem 1-6.(which is the book problem, no need for the R homework.)Please give me as much detail as you can. Thank you very much. Assignment: linear statistics problems sta_106_winter_2017_hw_2_due_january_26th.pdf STA 106 Winter 2018 Homework 2 Due Friday, Jan 26th (b) Describe what the values in (a) represent in words. (c) Find SSTO, SSE, SSA (d) Find d.f.{SST O}, d.f.{SSA}, d.f.{SSE} Book Homework (does not require R) (e) Find MSTO, MSE, MSA. 1. A rehabilitation center researcher was interested in ex- 4. Continue with problem 2. amining the relationship between physical fitness prior to (a) Without using a confidence interval or hypothesis test, surgery and the time (in days) for successful completion of does it appear that all groups differ significantly from physical therapy. The fitness levels were measured as Beeach other? Explain. low Average ( group I), Average (group II), or Above Average (group III). Summary statistics follow: (b) State the distribution of Y?2· , being as specific as you can. Assume i = 2 corresponds to the Young group. I II III Overall (c) State the null and alternative hypothesis for testing if Sample mean 38 32 24 32 all population group averages are equal, and the cor6.88 Sample Std. Dev 5.48 3.46 4.43 responding test-statistic. Sample Size 8 10 6 24 (d) Estimate the p-value and interpret it in terms of the problem. Data Source: Applied Linear Statistical Models, Kutner, (e) State your conclusion in terms of the problem, assumNachtsheim, Neter, & Li. ing ? = 0.01. (a) Estimate all values of µi . (f) What two group means are most likely to differ from (b) Estimate the expected value of Yij for every value of i, j. each other (if any)? 5. Prove the following identities. You may assume the Single Factor ANOVA model (and its assumptions) hold. P (a) j eij = 0 for any i. P P (b) i j eij = 0 P P (c) i j (Y?i· ? Y?·· )(eij ) = 0 P (d) E{Y?·· } = µ· , where µ· = i nniTµi (c) Find SSTO, SSE, SSA (d) Find d.f.{SST O}, d.f.{SSA}, d.f.{SSE} (e) Find MSTO, MSE, MSA. 2. Continue with problem 1. Assignment: linear statistics problems (a) Based on the sample values, would you conclude that the variance for each group is constant? Why or why not. (e) ? 2 {Yij } = ?2 (b) What group appears to have the fastest recovery time? 6. Answer the following questions with TRUE or FALSE. You Do you believe it is statistically significantly faster should explain your answer as practice for an exam. than the group that has the slowest recovery time? (a) In general, for a particular population, the larger nT , Without a confidence interval or hypothesis test, exthe larger SSTO is. plain your answer. (b) If we reject the null hypothesis, we may always con(c) State the null and alternative for testing if the popuclude there is evidence to suggest that all population lation means are all equal. means are different from each other. (d) Find the value of the test-statistic, and the approxi(c) To reduce the probability of a Type I error, we would mate the p-value for the test in (c). want to use the lowest value of ? possible. (e) State your conclusion in terms of the problem if ? = (d) It is possible for SSE to equal 0. 0.01. 3. A consumer organization studied the effect of age of automobile owner on cash offer for a used car (in hundreds of dollars). The age groups were Young (Y ), Middle (M ), and Old (O). Summary statistics follow: sample mean sample std. dev sample size M 27.75 1.29 12 O 21.42 1.68 12 Y 21.50 1.73 12 Overall 23.56 3.38 36 Data Source: Applied Linear Statistical Models, Kutner, Nachtsheim, Neter, & Li. (a) Estimate the value of µi ? µ· for all values of i. 1 R Homework (requires some use of R) (e) What group appears to have the smallest variance (if any)? I. Assignment: linear statistics problems Online you will find the file Cancer.csv. The csv file has the following columns: IV. Continue with problem II. (a) Find the value of SSTO, SSA, SSE. Column 1. Survival: The survival time of the patient in days (b) Find the value of MSTO, MSA, MSE. Column 2. Organ: The organ where cancer was present Stomach, Bronchus, Colon, Ovary, Breast (c) Find the value of the test-statistic, and the corresponding p-value. Data Source : From the article Supplemental Ascorbate in the Supportive Treatment of Cancer: Reevaluation of Prolongation of Survival Times in Terminal Human Cancer by Ewan Cameron and Linus Pauling, Proceedings of the National Academy of Sciences of the United States of America, Vol. 75, No. 9 (Sep., 1978), pp. 4538-4542. (d) State your conclusion in terms of the problem if ? = 0.05. (e) Interpret your p-value in terms of the problem. (a) Create a group box plot of Survival by Organ type. Does there appear to be significant differences in the groups? Explain your answer. (b) Find the sample averages of Survival by Organ type. Do you believe you would reject the null hypothesis of Single Factor ANOVA based on these values? Explain. (c) Do you believe the standard deviations of each population are equal? Explain. (d) What level of ? would you suggest if concluding that the true average survival time was equal when in reality it was not, would be considered the most severe error? II. Continue with problem I. (a) Find the value of SSTO, SSA, SSE. (b) Find the value of MSTO, MSA, MSE. Assignment: linear statistics problems (c) Find the value of the test-statistic, and the corresponding p-value. (d) State your conclusion in terms of the problem if ? = 0.05. III. Online you will find the file Hawks.csv. The csv file has the following columns: Column 1. Wing: Length (in mm) of primary wing feather from tip to wrist it attaches to Column 2. Species: CH=Coopers, RT=Red-tailed, SS=Sharp-Shinned The goal is to assess if these hawks can be easily distinguished by the length of their wing feathers. Source: Professor Bob Black at Cornell College (a) Find the standard deviation by groups. (b) Make histogram of wing feather length by group. (c) Do you believe that the assumption of equal variance by group is met? Explain your answer. (d) What group appears to have the largest wing feather length (if any)? 2 Get a 10 % discount on an order above $ 100 Use the following coupon code : NURSING10