Report

Homework 6 results 1.a Y = 150X + 200 Y = 200 + 150X Six minutes of flight . . . Y = 150*6 + 200 Y = 1100 1.b. Car rental Y = .06X + 29 Y = 29 + .06X Rental for 200 miles . . . Y = .06 * 200 + 29 Y = $41.00 2.a. Net loss of $20. Loss of $40 for membership plus $20 savings on $100 spent. 2.b. Spending Savings 0 100 200 300 0 20 40 60 400 80 2.c.: Must spend $200 for membership to be worthwhile. 2.d.: The function is linear because the change in Y is constant across all values of X. For every $100 spent, exactly $20 saved. 2.e. Amount spent = X Amount saved = Y Y = .2X - 40 3.a. Tobacco production 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 y = -0.0606x + 122.28 R² = 0.8244 0.200 0.000 1985 1990 1995 2000 2005 2010 3.b. Predicted 2012 production, equation method Y = -.0606 * 2010 + 122.28 Y = 0.353 billion pounds 3.b. Predicted 2012 production, trendline extension method 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000 1985 1990 1995 2000 y = -0.0606x + 122.28 R² = 0.8244 2005 2010 2015 3.c. Confidence in prediction 3.c. Confidence in prediction Pro: • Strong R-squared • Near-term forecast Con: • Imperfections in fit to trendline • Possible shift in trend in last four years 4.a. Percentage smokers 35.0 30.0 25.0 20.0 15.0 y = -0.4397x + 902.33 R² = 0.9494 10.0 5.0 0.0 1980 1985 1990 1995 2000 2005 2010 4.b. Prediction of percentage smoking in 2010, equation method Y = -.4397 * 2010 + 902.23 Y = 18.4% 4.b. Prediction of percentage smoking in 2010, trendline extension method 35.0 30.0 25.0 20.0 15.0 10.0 y = -0.4397x + 902.33 R² = 0.9494 5.0 0.0 1980 1985 1990 1995 2000 2005 2010 2015 4.d. Prediction of percentage smokers in 1953 Y = -.4397 * 1953 + 902.23 Y = 43.5% 4.d Confidence in prediction 4.d Confidence in prediction Pro: • Strong fit, R-squared Con: • Many years between 1953 and 1983, so many possible significant economic and social changes 4.e. Prediction when 100 percent smokers 100 = -.4397 * X + 902.23 100-902.23 = -.4397 * X -802.23/-.4397 = X 1824 = X 5.a Main point of article Projections of the percentage of the population who will be obese in 40 years is quite dubious if not totally bogus. 5.b Relevance to linear models It makes exactly the same point about projections far into the future as we considered with regard to the number of motor vehicles and consumption of coal