A professional hockey player is about to become a free-agent,…
Question A professional hockey player is about to become a free-agent,… A professional hockey player is about to become a free-agent, meaning he can play for any team he wishes. Having taken Statistics 217 as a student at U of C, he knows how powerful statistics can be when making decisions when faced with uncertainty.He wishes to use the statistical skills acquired during this `Stat 217′ days to see if the value of his free-agency contract depends on the length of the contract. That is, can he express the total value of the contract as a linear function of the number of years it is good for? The model he proposes isContractValuei = β0 + β1Lengthi + eiwhereLengthi – is the length, in years, of the contract awarded to a NHL player i after he became a free agentContractValuei – is total value of the contract awarded to a NHL player i, in millions of $.He looked at the free agent contracts of n=40 NHL players, and assumes that the value of one contract does not dictate the value of another. He ran a regression in Minitab getting the following output:Regression Analysis: Contract$ versus Duration PredictorCoefSD CoefTPConstant-7.7392.150 Duration5.82140.6245 S = 5.4836 R-Sq = Analysis of Variance SourceDFSSMSFPRegression Residual Error 1142.66 Total393755.5 Using the partial Minitab output, answer the questions below.(a) Estimate the model. Use three-decimals your answer.ContractValuei^ = equation editor + equation editor Lengthi(b) Find the coefficient of determination. Expresses as a percentage, and use two decimal places in your answer.r2= equation editor %(c) He wishes to test, at α=0.05, if the value of a free-agent contract is linearly dependent on the length of the contract, in a positive way. What would be his statistical hypotheses?A. H0:β1≥0HA:β1<0B. H0:β^1≥0HA:β^1<0C. H0:β^1=0HA:β^1>0D. H0:β1=0HA:β1>0E. H0:β1=0HA:β1<0F. H0:β1=0HA:β1≠0G. H0:β^1≥0HA:β^1≠0(d) Using the T-test, test the statistical hypotheses determined in (c). Find the value of the test statistic, using two decimals in your answer.Tcalc = equation editor (e) If he is to test the statistical hypotheses in (c) at α=0.01, he would conclude that the data he collected suggests that the ? total value of the contract length of the contract ? can cannot be expressed as a ? positive not positive negative linear function of the ? total value of the contract length of the contract .(f) For each additional year on an NHL free agency contract, he can be 95% confident that total value of the contract will ? increase decrease by ? a mean a median none of these of anywhere between equation editor million $ to equation editor million $.(Use two decimals in your answers in part (f).)(g) The Phoenix Coyotes are offering this player a 5-year contract, and in considering the offer our NHL free agent would like to find the mean total value of an NHL free agency contract that has a duration of 5 years. With 95% confidence, find such an interval.Note: You will need ∑i=140Lengthi=126 and ∑i=140Lengthi2=474Lower Bound = equation editor $millions (use two decimals in your answer)Upper Bound = equation editor $millions (use two decimals in your answer)Complete the statement below regarding the most important condition of the model estimation:(h) To incorporate this prediction model, the ? distribution of the contract length distribution of the value of the contract standard deviation in the contract length standard deviation in the value of the contract is assumed to be ? the same for all contract lengths. the same for all contract values. Normally distributed. right-skewed. Math Statistics and Probability STAT 217 Share QuestionEmailCopy link Comments (0)
