Homework 11.1 In 1 6, match each scatterplot with the appropriate correlation coefficient. a) +1 b) +0.8 c) +0.3 d) 0 e) -0.6 f) -0.9 1. 2. 3. 4. 5. 6. Match each graph with a description of its correlation coefficient: positive, negative, or almost zero. 7. 8. 9. Turn Page Revised: 3/27/2012 7
Homework 11.1 (cont d.) 10. Which correlation coefficient could match the graph? 1) -0.9 2) -0.3 3) 0.6 4) 1 11. Which of the following is a true statement? 1) The line of best fit always passes through each of the given data points. 2) The line of best fit must have a correlation coefficient of +1 or -1. 3) A correlation coefficient of -1 means that there is no correlation. 4) If the correlation coefficient is negative, the line of best fit has a negative slope. 12. Which of the following correlation coefficients most clearly represents a linear relationship for a given set of data points? 1) -0.89 2) -0.52 3) 0.58 4) 0.76 13. Which of the following correlation coefficients would indicate no significant linear relationship for the independent and depended variables in a data set? 1) -1 2) -0.52 3) 0.15 4) 0.90 Consider the paired variables and decide whether they have a positive correlation, a negative correlation, or almost zero correlation. 14. The number of bedrooms in a family home and the number of years the family has lived in the home. 15. The age of a child and the number of years of school that a child has attended. 16. The speed at which a car is driven and the distance traveled in a 6-hour period. 17. The age of a nonclassic car and its value for trade-in. 18. The waiting time at a restaurant and the number of entrees offered. Revised: 3/27/2012 8
Homework 11.2 1. Which equation models the data in the accompanying table? Time in hours, x 0 1 2 3 4 5 6 Population, y 5 10 20 40 80 160 320 (1) y = 2x + 5 (2) 2 x y (3) y = 2x (4) y 52 x 2. Write a power function rounded to the nearest ten-thousandth whose graph passes through the points (3, 8) and (6, 17). 3. Find an exponential model for the data: (0, 17.56), (1, 16.03), (2, 14.64), (3, 13.36), (4, 12.20), (5, 11.14), (6, 10.17). Round to the nearest hundredth. 4. Using the data at the right. X 2 4 5 6 8 Y 3 1 0-1 -3 a) Find the equation of the regression line based on the data below b) What is the correlation coefficient? Review: 5. For which pair of data would you expect a negative correlation? a) The number of hours studied for a test and grades on that test. b) ages of husbands and wives c) sale price of an item and number of units of that item sold d) income and shoe sizes of adults 6. For which pair of measurements would you expect no significant correlation? a) hand size and shoe size. b) income and education. c) car weight and the number of miles it can travel on 1 gallon of gasoline. d) bowling scores and number of traffic tickets. 1Revised: 3/27/2012 1
Homework 11.3 Time (min) Temp ( F) 0 179.5 5 168.7 8 158.1 11 149.2 15 141.7 18 134.6 22 125.4 25 123.5 30 116.3 34 113.2 38 109.1 42 105.7 45 102.2 50 100.5 Data: The data at the right shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180 F. a) Complete the scatterplot for the data given. b) Determine an exponential regression model equation to represent the data. Round equation answers to the nearest thousandth. Also write the correlation coefficient rounded to the nearest ten-thousandth. Exponential equation: Correlation coefficient: good fit? c) Graph the equation on the calculator. Based on the new equation (from answer b), what is the initial temperature of the coffee, rounded to the nearest tenth? (**hint: where is x = 0?) d) When is the coffee at a temperature of 106 F, rounded to the nearest hundredth of a minute? e) What is the predicted temperature of the coffee after 1.5 hours, rounded to the nearest tenth of a degree? f) In 1992, a woman sued McDonald's for serving coffee at a temperature of 180 that caused her to be severely burned when the coffee spilled. An expert witness at the trial testified that liquids at 180 will cause a full thickness burn to human skin in two to seven seconds. It was stated that had the coffee been served at 155, the liquid would have cooled and avoided the serious burns. The woman was awarded over 2.7 million dollars. As a result of this famous case, many restaurants now serve coffee at a temperature around 155. How long should restaurants wait (after pouring the coffee from the pot) before serving coffee, to ensure that the coffee is not hotter than 155, rounded to the nearest hundredth? 1Revised: 3/27/2012 5
Homework 11.4 **Covers 2 pages!!!** 1. For each pair of data values below, tell whether you would expect positive, negative, or zero correlation. a. Number of hours studied for a test versus the grade on the test. b. Income versus shoe sizes of adults. c Movie ratings (R, PG, G) versus movie popularity. d. Height versus arm span 2. The relationship of a woman s shoe size and length of a woman s foot, in inches, is given in the accompanying table. Woman's Shoe Size 5 6 7 8 Foot Length (in) 9.00 9.25 9.5 9.75 The linear correlation coefficient for this relationship is (1) 1 (2) 1 (3) 0.5 (4) 0 3. Which graph represents data used in a linear regression that produces a correlation coefficient closest to 1? (1) (2) (3) 4. The accompanying table shows the boiling points of water at different altitudes. a. Make a scatter plot of the data. Location Altitude, h (km) Boiling Point, t, (C) Wellington, New Zealand 0 100 Banff, Alberta, Canada 1.38 95 Quito, Ecuador 2.85 90 Mt. Logan, Canada 5.95 80 b. Estimate a and b correct to the nearest hundredth. Then write an equation of the line h = at + b that best fits the data. c. Write the correlation coefficient to the nearest thousandth. Turn Page 1Revised: 3/27/2012 8
5. The populations of the United States in the years 1900, 1950, 1980, and 1999 are shown in the accompanying table, where t=0 represents the year 1900. Year 1900 1950 1980 1999 a. Determine an exponential function y=ab t Population (millions) 76.2 151.3 226.5 272.7 that best fits the data in the table. Estimate a and b to the nearest thousandth. b. If this growth relationship continues, predict the U.S. population in 2020, to the nearest tenth of a million. c. If this growth relationship continues, in what year will the U.S. population exceed 400 million for the first time? 6. According to recent surveys, the percentage of new plant and equipment expenditures by US manufacturing companies on pollution control is as shown: 1975 1980 1981 1984 1987 9.3 4.8 4.3 3.3 4.3 a. Use a linear regression model to find the line of best fit. b. Estimate the figure for 1985. (Round your answer to one decimal place.) Day 11.4 HW Review Answers 1a) pos b) zero c) debatable d) pos 2) 1 3) 3 4b) y = -0.30x + 29.79 c) -0.9997 5a) y = 77.322(1.013) x b) 364.3 million people c) 2027 6a) y = -0.434729064x +866.5721675 b) 3.6 plant and equip expend. 1Revised: 3/27/2012 9
Day 5 Review for Quest 1. Which scatter diagram shows the strongest positive correlation? 2. A linear regression equation of best fit between a student s attendance and the degree of success in school is h = 0.5x + 68.5. The correlation coefficient, r, for these data would be (1) 0 r 1 (2) 1 r 0 (3) r = 0 (4) r = 1 3. A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are returned to the box, and then the process is repeated. The accompanying table shows the number of trials and the number of coins returned to the box after each trial. Trial 0 1 3 4 6 Coins Returned 1,000 610 220 132 45 a. Write an exponential regression equation, rounding the calculated values to the nearest ten-thousandth. b. Use the equation to predict how many coins would be returned to the box after the eighth trial. 4. Kathy swims laps at the local fitness club. As she times her laps, she finds that each succeeding lap takes a little longer as she gets tired. If the first lap takes her 33 seconds, the second lap takes 38 seconds, the third takes 42 seconds, the fifth takes 50 seconds, and the seventh lap takes 54 seconds, state the power regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using your written regression equation, estimate the number of seconds that it would take Kathy to complete her tenth lap, to the nearest tenth of a second. 2Revised: 3/27/2012 0
5. The data in the accompanying table show the growth of cellular phone subscriptions in the United States from 1993 to 1999. Year Subscriptions a. Find an exponential curve that best fits the data, where x=0 (millions) represents the year 1990 and y is the number of cell phone 1993 16.0 subscribers. Approximate a and b to the nearest thousandth. 1995 33.79 1996 44.04 1997 55.31 1999 86.05 b. Use the model to estimate the number of cellular phone subscribers in 1998. 6. A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shows a random sample of sales and location data. a. Write a linear regression equation that relates the price of a cottage to its distance from the beach, rounded to the nearest ten-thousandth. b. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach. Number of Blocks from the Beach (x) Price of Cottage (in thousands) (y) 5 $132 0 $310 4 $204 2 $238 1 $275 7 $60.8 Day 5 Classwork Review Answers 1) 1 2) 1 3a) y = 1018.2839(.5969) x b) 16 coins 4) y = 32.35x 0.26, 58.9sec 5a) y = 7.746(1.319) x b) 70.964 million people 6a) y = -34.7397x + 313.3091 b) $209,090 2Revised: 3/27/2012 1