Problem 4: Standing Tall is a roofing contractor of houses. Roofing normally is Done two months after the start of a house construction. Initially he relied on a simple linear trend regression forecast using just the months of the year and the number of roofing jobs generated. He felt there was something lacking in his forecasts. He decided to get the city hall housing permits per month to check the number of Jobs generated. 1. Set up the simple linear trend regression forecast using months and number of jobs. Is the regression model a good model? Why or why not? 2. Setup another model using months, permits and jobs. Determine if it is a good model 3. If so, determine the number of jobs generated for January the following year if 330 permits were issued. Month Permits Jobs Month Jobs 1 323 19 19 2 359 17 2 17 3 396 24 3 24 4 421 23 4 23 457 28 28 472 32 32 7 446 34 7 34 8 407 37 8 37 9. 374 33 33 10 343 30 10 30 11 311 27 11 27 12 277 22 12 22

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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?

Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300