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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The following table gives the data for the grades on the midterm exam and the grades on the final exam. Determine the equation of the regression line, yˆ=b0+b1x�^=�0+�1�. Round the slope and y-intercept to the nearest thousandth. Grades on Midterm and Final Exams Grades on Midterm 7171 6262 7878 9494 8383 8181 8080 9494 8585 6262 Grades on Final 8888 7979 8888 9191 8080 7070 7171 9393 6565 7777
- Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes. These data provided the estimated regression equation ŷ = 28,240 − 1,419x. For these data, SSE = 7,209,342.96 and SST = 50,969,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance. -Find the value of the test statistic. (Round your answer to two decimal places.)The following table shows the annual expenditures, in dollars, per customer unit for residential landline phone services and cellular phone services in the United States in the given year.† Year Landline Cell 2004 592 378 2006 542 524 2008 467 643 2010 401 760 Calculate the regression line for each type of service. (Let t be the time in years since 2004, L be the operating revenue of landline phone services and C be the expenditure of cellular services. Round your regression parameters to two decimal places.) L(t) = C(t) = Determine the expenditure level at which the two lines cross. Round your answer for the expenditure level to one decimal place. million dollarsConsider the following scenario for Questions 6 through 9: The City of Bellmore’s police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 What is the IV? What is the DV? If the mileage increases by one mile, what is the predicted increase in maintenance costs? If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
- For Data Set 9 in Appendix B, “Bear Measurements,” we get this regression equation: Weight = -274 + 0.426 Length + 12.1 Chest Size, with R2 = 0.928. Interpret the multiple coefficient of determination – what does this value tell us?For items 1 - 5, use the data below that gives the humerus bone length (in cm) and height (in inches) for a sample of female skeletons. [The data was provided by Dr. Ayers-Darling, former professor at MVCC.] humerus (cm) height (in.) 32.6 66 28.0 60 29.9 62 30.5 63 31.2 64 29.9 62 29.1 61 29.5 62 29.8 62 28.5 61 Find the slope of the least-squares regression line that relates humerus length to female height. Express its value to three decimal places (to the nearest thousandth).__________________________ Find the y-intercept of the least-squares regression line that relates humerus length to female height. Express its value to three decimal places (to the nearest thousandth).___________________________ The least-squares regression line relating two variables x and y is given by . Find the predicted value of y if x is 2.___________Consider the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week. hours/weekx Gradey 5 58 8 63.2 8 73.2 9 68.6 9 70.6 11 68.4 13 81.2 14 86.6 17 100 20 100 The regression equation is y=3.04⋅x+42.33y=3.04⋅x+42.33.Explain what the value of the slope means in this situation, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week.Explain what the value of the y-intercept means in this situation.What is the predicted value for the final grade when a student spends an average of 15 hours each week on math?Grade = Round to 1 decimal place.
- For the simple regression equation (a), conduct an individual significance tests at the 5% significance level to determine if SQFT is a significant predictor of Price. (Check photo for data)The regression line for a data set showing the monthly utility bill U in a certain city versus the square footage F of the residence is given by U = 0.2F − 100 dollars. What monthly utility bill would be expected for a 2500 square foot home in this city? $Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1=married, 0=otherwise), a dummy variable for head of household (Head: 1=yes, 0=no) and a dummy variable for management position (Manager: 1=yes, 0=no). We shall call this Model 1. The coefficient of partial determination (R2Yj.(All variables except j)) of each of the six predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given. Refer to model 1. Which of the following is the correct null hypothesis to test…