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STAT 301 Homework 9 (Graded)




Question;This is an assignment and the outcome of your attempt will be assessed towards yourperformance in this course. When you are ready, enter your answers and click submitanswers. You cannot go backwards once you have submitted a page.If you would like to answer these questions offline, print this page and then bookmark it to bereturned to your e-workbook home page. Please note that any answers you have entered on thispage will not be kept with your bookmark. If you bookmark this page, you must return to it andsubmit your answers before the end date of this assignment.You will know that your answers are stored to the database and that you have finished theassignment when you see this message displayed: 'You have finished the assignment'.1 of 11ID: MST.SLR.REE.03.0040[6points] points]A biologist is studying the levels of heavy metal contaminants among a population of the South Nakaratuan ChubbyBat. The biologist is interested in constructing a simple linear regression model to investigate the relationshipbetween weight of an animal and the level of heavy metal contamination. In the proposed regression model the levelof contaminant is the response variable and weight is the explanatory variable. The contaminant level is measured inparts per billion (ppb) and weight in grams.A random sample of 20 individuals is selected and measurements are taken.Contaminant study inSouth Nakaratuan Chubby BatContaminant level(ppb)Weight(g)181149132109153115189145169146186146154131155133135121136113114105144123165139134102134105Download the data198146116110187139120100224107Plotting the data, the researcher notices an obvious outlier. They decide to do the regression analysis with andwithout the outlier and compare the results.Calculate the slope (b1) and intercept (b0) of the simple regression equation using the data provided. Give youranswers to 2 decimal places.a) Slope = b1 =b) Intercept = b0 =Find the proportion of variation in the values of contaminant level that is explained by the regression model. Giveyour answer as a decimal to 2 decimal places.c) R2 =Repeat this process omitting the outlier:d) Slope = b1 =e) Intercept = b0 =Find the proportion of variation in the values of contaminant level that is explained by the regression model. Giveyour answer as a decimal to 2 decimal places.f) R2 =2 of 11ID: MST.SLR.AV.06.0010b[2points] points]The Mean Corporation has been commissioned to conduct a study is into therelationship between the population of a city and the number of motor vehicleaccidents in the city per year. A linear regression model is to be constructed. Inthe proposed regression model, number of motor vehicle accidents per year is theresponse variable and population of the city is the explanatory variable.A random sample of 20 cities is selected and measurements are observed.Population('000s)No. accidentsper year2,7006,6922,3405,8794802,4732,5907,1102,4706,404Download the data1,5404,5722,2605,8622,1404,9819503,7582,1406,4321,8104,3673,1306,7172,2205,4101,7004,7674202,5301,6204,2562,1204,4017502,6371,1002,9951,1903,454a) Calculate the point prediction for the value x = 2,500. Give your answer as a whole number.^y=b) Give the 95% prediction interval for the value x = 2,500. Give your answers as whole numbers.^y3 of 11ID: MST.SLR.ALR.02.0020[1point] point]A study was conducted into the relationship between the age in years of a person and their average weekly after taxincome.You have been supplied with the following information regarding a regression model that had been developed as partof the study.Regression analysissample intercept652.95sample slope3.75A particular observed value from the data is:x = 31, y = 774.52Calculate the residual of this observed value of the response variable. Give your answer to 2 decimal places.residual =4 of 11ID: MST.SLR.REE.06.0020[1point] point]The following table shows the average petrol price and the number of online shopping orders over a given month:Petrol Price and Online ShoppingAverage Petrol Priceper gallon over a month ($)Number of OnlineShopping Orders2.31252,7442.772,8282.2152,3193.633,5153.28753,0754.8155,0282.3252,3091.6352,3162.77253,6211.8351,741The relationship between the average petrol price and the number of online shopping orders in a given month isproposed to follow the simple regression equation below: show variables^y = b0 + b1xCalculate the proportion of variability in the number of online shopping orders that is not explained by the averagepetrol price. Give your answer as a percentage to 1 decimal place.Proportion =5 of 11%ID: MST.SLR.REE.04.0020b[3points] points]The regression equation:^y = 5 + 1.2xwas calculated from a sample. It is part of a regression model that has been developed in order to predict the scorein an end-of-year exam based on the score in a mid-year exam for a particular university course. In the sample, midyear scores ranged from 50 to 80.Select whether or not each of the following conclusions are correct from the regression analysis:Correcta)For an increase by one in the mid-year score, the predicted increase in end-ofyear score is 1.2.b)If a student achieves a score of 45 in the mid-year exam then we know that thestudent will achieve a score of 59 in the end-of-year exam.Notcorrectc)If a student achieves a score of 60 in the mid-year exam then we know that thestudent will achieve a score of 77 in the end-of-year exam.6 of 11ID: MST.NDM.CC.08.0010[1point] point]An investigation has been conducted to determine whether there is arelationship between the salary paid to a Chief Executive Officer (CEO)and the productivity of that CEO as measured by the change in profitsfrom the time the CEO was employed.The scatter plot plots the salary paid (x) against the change in profits (y)of a sample of CEOs. Without doing any calculations and according onlyto this scatter diagram, a reasonable coefficient of correlation (r)between x and y would be:r = 1.57r = 0.33r = -1.94r = -0.537 of 11ID: MST.SLR.TM.01.0030[1point] point]It has been hypothesised that there is a linear relationship between the average annual interest rate and the volumeof car sales, and that relationship can be represented as follows: show variables^y= b0 + b1xThe following table lists the average interest rates recorded in a particular year and the corresponding number of carsales:Interest Rates and Car SalesInterest Rate (% per annum)Car Sales Volume (millions)55.435.75.4694.84.9865.64.6828.74.5796.94.2534.24.9848.24.7347.64.2024.65.332Using the data provided, and at = 0.05, the null hypothesis that a significant linear relationship between theaverage annual interest rate and the volume of car sales does not exist is. You may find thisStudent's t distribution table useful.8 of 11ID: MST.SLR.REE.03.0030[2points] points]A study is conducted to determine the simple linear regression relation (if any) between average temperature over aweek and ice-cream sales in a particular city. The following table provides the regression data required to constructthe model:Average Temperature and Ice-cream SalesAverage Temperatureover a Week (F)Weekly Ice-cream Sales($'000s)62204.45346165.30382252.30381251.19851177.48841152.83856189.43331128.24863206.89846165.51355187.79893279.688Calculate the slope (b1) and intercept (b0) of the simple regression equation using the data provided. Give youranswers to 2 decimal places.(a) Slope = b1 =(b) Intercept = b0 =9 of 11[2points] points]Two variables (A and B) are hypothesised to have a linear relationship with one another, as represented by thefollowing equation:AID: MST.SLR.REE.07.0020= 0 + 1B +Data was gathered for these two variables and the correlation coefficient (r) was calculated to be -0.92.Select all from the following statements that are true:Variable A is known as the explanatory variable, and variable B is known as the response variable.Variable B causes variable A since B is the independent variable.0 is known as the sample intercept.The proportion of variability in A that is explained by the regression model is equal to 84.64%.The linear regression line provides a strong fit to the observed data.Causation between A and B cannot be implied from the correlation that exists between them.The graph of the linear relationship between A and B slopes up.10 of 11ID: MST.SLR.ALR.01.0030c[1point] point]You have constructed a simple linear regression model and are testing whether the assumption of normality of theresiduals is reasonably satisfied.Select the scatter plot that indicates normality of the residuals:11 of 11ID: MST.DCP.GRR.03.0040[1point] point]A cinema manager wishes to investigate the pattern of ticket sales over the different days of the week. Starting on aMonday, she records the number of tickets sold each day for one week. The results are recorded belowDayTickets sold1321254534124901512906121571063In the time-series plot below, only four of the values have been marked. Drag the three red markers onto the plot tocomplete it and represent the data for all seven days.


Paper#61594 | Written in 18-Jul-2015

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