# Scatter Plots and Line of Best Fit

## 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.

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