Over time, according to records kept by the Environmental Protection Agency (found at www.epa.gov), recycling rates have increased from 10% of municipal solid waste generated in 1980 to 16% in 1990, to 29% in 2000, and to 34% in 2009. Meanwhile, disposal of waste to a landfill has decreased from 89% of the amount generated in 1980 to 54.3% of solid waste in 2009. The prediction equation (or least- squares prediction equation) for the percent of solid waste recycled by Americans is y = 0.932x - 1837 where y = percent of solid waste recycled and x is the year. (a) Graph these data (percent recycled vs. year), leaving room at both ends for past and future years. Draw the line given by the prediction equation on your graph also. (b) Is the slope positive or negative? What does the slope tell us about the rate of recycling over the past 30 years? (c) Use the prediction equation to determine the x-intercept. What does this value tell you? Use your graph to help you verify your answer by plotting this point. (d) During what year will recycling theoretically reach 50% according to this model? Plot this point on your graph. (e) Theoretically, will recycling ever reach 100%? Practically speaking, is that really possible?

The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four predictor variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table. Time Miles Load Speed Oil 7.7 42.9 22.0 44.0 16.0 0.8 98.3 20.0 47.0 34.0 6.3 61.1 22.0 62.0 15.0 E Click here for the Excel Data File b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Time = Miles Load Speed oil + + d. What is the predicted time before the first engine overhaul for a particular truck driven 60,000 miles per year with an average load of 25 tons, an average driving speed of 53 mph, and 21,000 miles…

A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y = -13258.594 + 2.422X,, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000 20000 -20000 -20000 -40000 40000 TO 20 Index Normal Quantile Residuals vs. Program Per-Year Tuition ($) Residuals Predicted Values vs. Residuals Predicted Values 20000 140000- 120000- 100000 80000- -20000 60000 -40000 40000- 30000 50000 4000 Program Per-Year Tuition ($) 20000 60000 70000 -20000 20000 Residuals ..... a) To evaluate whether the assumption of linearity…

An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Click here to view the weight and gas mileage data. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Car Weight and MPG (Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.) Weight (pounds), x Miles per Gallon, y 3806 16 3796 15 2669 24 3520 18 3361 21 2911 22 3808 18 2612 24 3375 19 3737 16 3320 19