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STATS Few Problems Assignment

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Question;1.) During the years 20052009, the world record for the 100-meter dash was repeatedly broken as neverbefore. The years and corresponding record times are in data file XR17008 and shown in the table.Using x = 1 through 5 to represent years 20052009, fit a second-order polynomial model to the data.(SOURCE: Karen Rosen, "9.58: Bolt Strikes Again at Worlds," USA Today, August 17, 2009, p. 1C.)Please round your answers to 2 decimal places.a. The estimate of the world record time for the 100-meter dash in 2014 is seconds2.) This exercise requires a computer and statistical software. The data mentioned below can be found inseveral formats on your Premium Website under "Chapter datasets".An early edition of Car and Driver magazine reported the engine horsepower, top speed (mph), curbweight (pounds), and 060 mph acceleration time (seconds) for a selection of automobiles that rangedfrom large American "muscle cars" to small economy imports. The data are in file XR17009. Fit a thirdorder polynomial model (using top speed (mph) as the dependent variable and horsepower as theindependent variable) to predict the top speed for a car with 170 horsepower. (SOURCE: 1964 Car andDriver Yearbook, pp. 14-63.)Please round (a) through (e) to 4 decimals, and (f) to the nearest whole number.a. The p-value of the hypothesis test of whether the regression equation is significant is.b. The estimated intercept is.c. The estimated coefficient of horsepower is.d. The estimated coefficient of horsepower2 is.e. The estimated coefficient of horsepower3 is.f. The estimated top speed of a car with 170 advertised horsepower is.3.) The regression model= 200 + 5x1 - 2x2 has been fitted to a set of data.a. If x2 = 10, the effect onof an increase in x1 of 1 unit is.b. If x2 = 20, the effect onof an increase in x1 of 1 unit is4.) This exercise requires a computer and statistical software. The data mentioned below can be found inseveral formats on your Premium Website under "Chapter datasets".Auto Rental News has reported U.S. operations data for 15 top rental-car companies. Using data file XR17016,with y = rental revenue (millions of dollars) for the most recent year of record, x1 = thousands of cars in service,and x2 = number of rental locations, fit a first-order model of the form E(y) = 0 + 1x1 + 2x2 (SOURCE: Wall StreetJournal Almanac 1999, p. 649.)Please round (a) through (c) to 2 decimals, and (d) and (e) to 3 decimals.a. The estimated intercept is.b. The estimated coefficient of "Cars" is.c. The estimated coefficient on "Location" is.d. The p-value of the hypothesis test of whether the regression equation is significant is.e. The amount of variation in "Revenue" that is explained by the equation is. (express your answer as adecimal)5.)This exercise requires a computer and statistical software. The data mentioned below can be found in severalformats on your Premium Website under "Chapter datasets".Auto Rental News has reported U.S. operations data for 15 top rental-car companies. Using data file XR17016,with y = rental revenue (millions of dollars) for the most recent year of record, x1 = thousands of cars in service,and x2 = number of rental locations, fit the model E(y) = 0 + 1x1 + 2x2 + 3x1x2 (include an interaction term).Please round (a) to 4 decimals, and (b) to 3 decimals.a. The estimated coefficient on the interaction term is.b. The amount of variation in "Revenue" that is explained by the equation is.6.) The Air Transport Association has reported the following kinds of information describing 23 individual U.S.airlines for the most recent year of record: y = total operating revenue ($millions), x1 = number of aircraft and x2= number of employees. The data are in file XR17017. (SOURCE: Wall Street Journal Almanac 1999, p. 644.)Fit a first-order model of the form E(y) = 0 + 1x1 + 2x2Please round (a) to 1 decimal, and (b) through (e) to 3 decimals.a. The estimated intercept is.b. The estimated coefficient of x1 is.c. The estimated coefficient on x2 is.d. The p-value of the hypothesis test of whether the regression equation is significant is.e. The amount of variation in "Revenue" that is explained by the equation is. (express your answer as adecimal)7.)The Air Transport Association has reported the following kinds of information describing 23 individual U.S.airlines for the most recent year of record: y = total operating revenue ($millions), x1 = number of aircraft and x2= number of employees. The data are in file XR17017.Fit the model E(y) = 0 + 1x1 + 2x2 + 3x1x2 (include an interaction term).Please round (a) to 5 decimals, and (b) to 3 decimals.a. The estimated coefficient on the interaction term is.b. The amount of variation in y that is explained by the equation is8.)For the Car and Driver information described in Exercise 17.9, it would seem reasonable that the number ofseconds required to accelerate to 60 mph would depend on both a car's weight and its horsepower. Further, itwould be logical to assume that horsepower and weight might interact. Using data file XR17009, with y = 0-60mph acceleration time (seconds), x1 = horsepower, and x2 = curb weight (pounds), fit a model of the form E(y) =220 + 1x1 + 2x2 + 3x1x2 + 4x1 + 5x2Please round your answers to 3 decimal places.a. The p-value of the hypothesis test of whether the regression is significant is.b. The R2 of the regression is. (express your answer as a decimal)9.) The dean of a law school has developed a regression equation for estimating the starting salary(thousands of dollars) of a new graduate on the basis of two independent variables: x1 = the score achieved onthe Law School Admission Test (LSAT) at the time of application, and x2 = whether the new graduate's positionis in the private sector (coded as 1) or the public sector (coded as 0). For the estimation = 25 + 0.1x2 + 30x2,the estimated the starting salary (in thousands of dollars) for a new graduate with an LSAT score of 160 who isentering the private sector is10.)A researcher has observed 50 automatic teller machine (ATM) users outside the gift shop of a museum, andthe data are in file XR17028. With y = amount withdrawn (dollars), x1 = time required for the transaction(seconds), and x2 = gender (1 = female, 0 = male), determine the linear regression equation for estimating thewithdrawal amount as a function of the two predictor variables.Please round your answers to 2 decimal places.a. The estimated intercept is.b. The estimated coefficient of x1 is.c. The estimated coefficient of x2 (gender variable) is11.)Forasmallsampleofsuburbanhomesrecentlysold,thesellingprice($),livingspace(squarefeet),andsuburbanarea(SunnyHaven,EasyAcres,orRollingHills)havebeenrecorded.Giventhedatashownhere,determinethelinearregressionequationforestimatingsellingpricebasedontheothervariables.Pleaseround(a)to2decimalsandround(b)and(c)tothenearestinteger.a.Anadditionalfootoflivingspacewilltendtocost.(Pleaseroundyouranswerto2decimalplaces)b.AhomeinSunnyHavenwilltendtocostmorethanahomeinRollingHills.c.AhomeinEasyAcreswilltendtocostlessthanahomeinRollingHills.12.)Followingdatatransformation,regressionanalysisresultsintheestimationequationlog =3.15+0.473logx1+0.354logx2.Transformthisequationtotheequivalentmultiplicativemodelwithestimationequation =b0x1b1x2b2(Thebaseofthelogarithmsis10.)Pleaseroundyouranswersto3decimalplacesa.b0=.b.b1=.c.b2=.13.)Note:Duringtheyears20052009,theworldrecordforthe100meterdashwasrepeatedlybrokenasneverbefore.TheyearsandcorrespondingrecordtimesareindatafileXR17008andshowninthetable.Usingx=1through5torepresentyears20052009,fitanexponentialmodel.(SOURCE:KarenRosen,9.58:BoltStrikesAgainatWorlds,USAToday,August17,2009,p.1C.)Pleaseroundyouranswersto2decimalplaces.a. Theestimatetheworldrecordtimeforthe100meterdashintheyear2014isseconds.14.)This exercise requires a computer and statistical software. The data mentioned below can be found in severalformats on your Premium Website under "Chapter datasets".Use logarithms with base 10. Auto Rental News has reported U.S. operations data for 15 top rental-carcompanies. Using data file XR17016, with y = rental revenue (millions of dollars) for the most recent year ofrecord, x1 = thousands of cars in service, and x2 = number of rental locations, fit a multiplicative model.(SOURCE: Wall Street Journal Almanac 1999, p. 649.) The estimated rental revenue for a company with80,000 cars in service and 2500 rental locations is.Please round your answer to 2 decimal places15.) Note: This exercise requires a computer and statistical software. The data mentioned below can be foundin several formats on your Premium Website under "Chapter datasets".Auto Rental News has reported U.S. operations data for 15 top rental-car companies. The data file isXR17016, with y = rental revenue (millions of dollars) for the most recent year of record, x1 = thousands ofcars in service, and x2 = number of rental locations. (SOURCE: Wall Street Journal Almanac 1999, p. 649.)Complete the following correlation matrix for the independent variables.Please round to 3 decimals. If there is no entry enter "0".Cars16.)The sales director for an industrial supplies firm has collected information describing the performanceand personal characteristics of 80 members of her sales force. The data in file XR17066 include the percent ofsales quota the salesperson achieved last year, age, number of years with the firm, and personal appearance(very neat, about average, or a little sloppy). In the data file, a very neat person is coded as neat = 1, average= 0, a person of average neatness is coded as neat = 0, average = 1, and a sloppy person is coded as neat =0, average = 0. With y = percent of sales quota, perform a linear regression using the other variables aspredictors.Please round (a) through (d) to 2 decimals, and (e) and (f) to 3 decimals.a. The coefficient of "Age" is.b. The coefficient of "Years with the firm" is.c. A person that is "very neat" will tend to have a quota performance that is percentage points greater than aperson who is "sloppy.d. A person that is "average" will tend to have a quota performance that is percentage points greater than aperson who is sloppy.e. The amount of variation that the regression equation explains is.f. The p-value of the hypothesis test of whether the regression is significant is.17.) The Dow Jones Global Indexes describe over 3000 companies worldwide that represent more than80% of the equity capital in the world's stock markets. Data file XR17068 shows the quarterly indexes for theworld as a whole, and indexes for the United States, the Americas, Europe, and the Asia/Pacific region over 23consecutive quarters. (SOURCE: Wall Street Journal Almanac 1999, p. 264.)Given that the dependent variable will be y = world index, construct a correlation matrix for the four possiblepredictor variables.Please round to 3 decimals.

 

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