Regression Problems Math The data for these problems is from Math 142 Dr Lacey Packet 118 1 A Tomahawk Cruise ship in the South Pacific misfires a missile The missile goes over the side of the ship and hits the water In the data x is the number of seconds after the missile is launched and y is the number of feet above water for the missile x 0 0 5 1 1 5 2 2 5 3 y 128 140 144 140 128 108 80 View the data in a stat plot Which function we studied might best fit this data Find the regression model and paste it to a function After how many seconds will the missile hit the water according to your model What does the model predict the height will be after 4 seconds 2 The table shows the amount of money in billions of dollars spent on pollution control in the U S for the years 1983 to 1986 Year 1983 1984 1985 1986 spent 61 8 68 9 74 6 78 7 in bill Let x be the number of years past 1983 View the data in a stat plot Find a cubic regression model What is r 2 Extend the data list to include 1987 81 5 1988 1989 86 1 91 3 Compare the cubic and quartic regression models Which is a better fit of the existing data What does each predict for 1990 3 A department store begins selling swimsuits in January The table shows the cumulative total number of suits sold by the end of each month Jan 4 Feb 12 Mar 25 Apr 58 May 230 June 439 July 648 Aug 748 Sept 769 Let x 1 be Jan x 2 be Feb etc View the data in a stat plot Which model would you choose What is the limiting total number of swimsuits sold according to this model 4 A company surveyed 1000 people who owned one of its washing machines The data shows the number of machines that had a first servicing x years after purchase Years before 1st service Number of machines 5 787 10 619 15 487 20 383 25 301 30 237 a Fit an exponential model to this data and write it down b Replace the y list with lny take the natural log of the numbers in the 2nd list and use this for list 2 What does the stat plot look like What model would you choose 5 The data shows the average brain weight as a of body weight for different ages x 0 2 y 11 8 4 6 8 10 12 14 16 7 6 5 4 5 4 3 5 3 25 We will fit an exponential model to this data But since exponential models level off at y 0 and this seems to level off at y 3 we will subtract 3 from all the y values to get a better fit Enter the x values in list 1 and the y values 3 in list 2 Do the exponential and quartic regression models Which fits the existing data better Which makes more sense especially for predicting the brain body weight at age 20
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