Statistics – Quadratic Models Practice Name: ____________________________________ Date: ____________________ Period: __________ 1) A scatter plot with either a positive or negative correlation can be better modeled by a _____________ equation. 2) A scatter plot that appears parabolic can be better modeled by a _____________ equation. 3) For the following data: create a scatter plot, determine whether the data could be modeled better by a linear model or a quadratic model, use the regression feature of a graphing utility to find the a model for the data, graph the model over the scatter plot, and create a table comparing the original data with the data given by the model. a. (0, 2.1), (1, 2.4), (2, 2.5), (3, 2.8), (4, 2.9), (5, 3), (6, 3), (7, 3.2), (8, 3.4), (9, 3.5), (10, 3.6) b. (-2, 11), (-1, 10.7), (0, 10.4), (1, 10.3), (2, 10.1), (3, 9.9), (4, 9.6), (5, 9.4), (6, 9.4), (7, 9.2), (8, 9) 4) For the following data: use the regression feature to find a linear model and quadratic model for the data, determine the coefficient of determination for each model, and use the coefficient of determination to determine which model fits the data better. a. (1, 4), (2, 6.5), (3, 8.8), (4, 10.6), (5, 13.9), (6, 15), (7, 17.5), (8, 20.1), (9, 24), (10, 27.1) b. (-6, 10.7), (-4, 9), (-2, 7), (0, 5.4), (2, 3.5), (4, 1.7), (6, -0.1), (8, -1.8), (10, -3.6), (12, -5.3) 5) The table shows the monthly normal precipitation P (in inches) for San Francisco, California. Month Jan Feb March April May June July Aug Sept Oct Nov Dec Precipitation 4.45 4.01 3.26 1.17 0.38 0.11 0.03 0.07 0.2 1.4 2.49 2.89 a. Create a scatter plot of the data. Let t represent the month with t = 1 corresponding to January. b. Use the regression feature to find a quadratic model for the data. c. Graph the model with the scatter plot d. Determine which month the normal precipitation in San Francisco is the least 6) The table shows the amounts A (in dollars) spent per person on the Internet in the USA from 2000 to 2005. Year 2000 2001 2002 2003 2004 2005 Amount 49.64 68.94 84.76 96.35 107.02 117.72 a. Create a scatter plot of the data. Let t represent the year, with t = 0 corresponding to 2000. b. A cubic model for the data is 𝑆 = 0.25444𝑡 3 − 3.044𝑡 2 + 22.485𝑡 + 49.55 which has an 𝑟 2 value of 0.99992. Graph this model over your scatter plot. Is the cubic model a good fit for the data? Explain. c. Use the regression feature to find a quadratic model for the data and identify the coefficient of determination. d. Graph the quadratic model with the scatter plot. Is the quadratic model a good fit for the data? Explain. e. Which model is a better fit for the data? Explain.
