SECTION 3.2 Building Linear Models from Data 155 19. Video Games and Grade-point Average Professor Grant Alexander wanted to find a linear model that relates the number h of hours a student plays video games each week to the cumulative grade-point average G of the student. He randomly selected 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative gradepoint average. Hours of Video Games per Week, h Grade-point Average, G 0 0 2 3 3 5 8 8 10 12 3.49 3.05 3.24 2.82 3.19 2.78 2.31 2.54 2.03 2.51 (a) Explain why the number of hours spent playing video games is the independent variable and cumulative gradepoint average is the dependent variable. (b) Use a graphing utility to draw a scatter plot. (c) Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation. (d) Interpret the slope of the line of best fit. (e) Predict the grade-point average of a student who plays video games for 8 hours each week. (f) How many hours of video game playing do you think a student plays whose grade-point average is 2.40? 20. Hurricanes The data at the top of the next column represent the atmospheric pressure p (in millibars) and the wind speed w (in knots) measured during various tropical systems in the Atlantic Ocean. (a) Use a graphing utility to draw a scatter plot of the data, treating atmospheric pressure as the independent variable. (b) Use a graphing utility to find the line of best fit that models the relation between atmospheric pressure and wind speed. Express the model using function notation. (c) Interpret the slope. (d) Predict the wind speed of a tropical storm if the atmospheric pressure measures 990 millibars. (e) What is the atmospheric pressure of a hurricane if the wind speed is 85 knots? Atmospheric Pressure (millibars), p Wind Speed (knots), w 993 50 994 60 997 45 1003 45 1004 40 1000 55 994 55 942 105 1006 40 942 120 986 50 983 70 940 120 966 100 982 55 Source: National Hurricane Center. 21. Maternal Age versus Down Syndrome A biologist would like to know how the age of the mother affects the incidence of Down syndrome. The following data represent the age of the mother and the incidence of Down syndrome per 1000 pregnancies. Draw a scatter plot treating age of the mother as the independent variable. Would it make sense to find the line of best fit for these data? Why or why not? Age of Mother, x Incidence of Down Syndrome, y 33 34 35 36 37 38 39 40 41 42 43 44 45 2.4 3.1 4 5 6.7 8.3 10 13.3 16.7 22.2 28.6 33.3 50 Source: Hook, E.B., Journal of the American Medical Association, 249, 2034–2038, 1983.
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