Scatter Plots and Line of Best Fit

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06.06 Assignment

Question 1

The table represents data collected on the time spent studying (in minutes) and the resulting test grade.

Time Spent Studying (min)	52	37	31	9	26	40	22	10	45	34	19	60
Grade on Test	95	84	72	58	77	86	72	43	90	81	62	98

Part 1: Create a scatter plot with the predicted line of best fit drawn on it. Determine the type of correlation (if any), and predict the model that will be used.
Part 2: Find the line of best fit for the data either by hand or using technology. Explain your method. Find the predicted score for each time listed in the table.
Part 3: Find the residuals, and decide if your model is a good fit. Explain your method. (If your model is not a good fit, complete Part 2 again with a different set of points or choose a different model.)

Question 2

Look back at the data from the New York Marathon.

Year	Competitors*	Year	Competitors*	Year	Competitors*
1976	2.1	1987	22.5	1997	31.4
1977	4.8	1988	23.5	1998	32.4
1978	9.8	1989	25	1999	32.5
1979	11.5	1990	25.8	2000	30
1980	14	1991	26.9	2001	24
1981	14.5	1992	28.6	2002	32.5
1982	14.3	1993	28.1	2003	35.3
1983	15.2	1994	31.1	2004	37.3
1984	14.6	1995	29	2005	37.6
1985	16.7	1996	29	2006	38.4
1986	20.5	* in thousands

Use this original data, but update it with the following information so that it is accurate through 2011. (The 2012 NY Marathon was cancelled due to the aftermath of Hurricane Sandy.) Use the entire data set (1976-2011) to answer all parts of Question 2.

Year	Competitors (in thousands)
2007	39.2
2008	37.9
2009	43.7
2010	44.8
2011	46.8

Part 1: Find a regression model for this new, updated data set (1976-2011). Explain your method.
Part 2: How well does it fit? Explain your answer and reasoning.
Part 3: Use your model to predict the attendance in 2017.