Math 253 - Chapter 9 Problems

Math 253 - Chapter 9 Problems - Chapter 9 Problems 4 a) The...

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Chapter 9 Problems 4 a) The years before 1925 are high leverage points and they b) It's probably appropriate, although the residuals are starting to increase in a regular pattern towards the end of the period. c) The slope says that the difference in ages at first marriage is steadily decreasing. Taking numbers from the graph indicates that the difference changes by about 1/4 year every 10 years. d) The data begin with 1975. Extrapolating to the year 0 is an extrapolation of over 1900 years from 20 years data. Not reasonable. The y intercept occurs when x = 0. If the data were to be traced back farther, say to 1700, the data points would be more likely to form a horizontal line than one with a negative slope. This change in behaviour is due to changing socio-economic conditions which are specific to the 20th century. 10 a) For every 10 mph increase in speed, the model predicts that the mileage will drop by 1 mpg. b) The y intercept assumes that the car is not moving, v = 0. The mileage at that speed is 0. The car just sits in the driveway with the motor running. c) The residuals are negative. The model overestimates the mileage. d) At 50 mph, the model predicts 27 mpg. From the graph, the e) At 45 mph, the predicted mileage is 27.5 and the residual is about 1 mpg. f) There is a strong, but not linear, association between speed and fuel econ g) A linear model is not appropriate. There is strong curvature in the line formed by the data, as shown in the residuals. 15 a) The association would be far stronger is humans were removed. Both slope and correlation would increase. The point associated with humans is far to the right which gives it a large amount of leverage. are all in a pretty straight line, so will have a large effect on R 2 . residual at 27 mpg is +2.5 mpg, i.e. , y - = 2.5. Then, y = + 2.5, so ŷ ŷ y = The actual mileage is y = + 1, so y = ŷ 28.5 mpg
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b) Human life spans are prolonged substantially by modern medicine. There is ample justification for removing humans from the list. c) The correlation coefficient is .85 and the straight line model accounts for 72% of the variation in the data. Moderately strong. d)
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This note was uploaded on 05/02/2008 for the course MATH 253 taught by Professor Weaver during the Spring '08 term at Idaho State University.

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Math 253 - Chapter 9 Problems - Chapter 9 Problems 4 a) The...

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