MAT109 Linear Function Review/Pre-Test Supplementary Assignment 4 – Linear Regression MATH&146 – Introduction to Statistics NSC/pmkurose 8/2021 Part A: Linear Function Review 1. a) It snowed 10” in 4 hours. Determine the average rate at which it snowed in inches per hour. b) A tree was 12” tall when it was planted. After 3 weeks, the tree was 16” tall. Determine the average rate at which the tree grew in inches per week (to the nearest hundredth of an inch per week). c) A man went on a diet when his weight reached 200 pounds. After 6 months, he weighed 180 pounds. Determine the average rate of weight loss in pounds per month (to the nearest tenth of a pound per month). d) At age 10, Mason was 130 centimeters tall. At 16, he was 175 centimeters tall. Determine Mason’s growth rate (from age 10 to 16) in centimeters per year. 2. Write an equation and sketch the graph for the described linear relation. a) Kenji started with $50 in his bank account, then deposited $10 per week. Let x = # of weeks and y = account balance. b) A tree is 10 inches tall when it is planted. It grows at a constant rate of 1.5 inches per month. Let x = # of months from when the tree was planted and y = the height of the tree. c) A snowball weighed 60 pounds when it started to melt. It melted at a constant rate of 4 pounds per hour. Let x = # of hours the snow had been melting and y = weight of the snowball. 3. A bathtub contained 45 gallons of water when the plug was pulled. Six minutes later, 36 gallons of water remained in the tub. Assume the bathtub drained at a constant rate (in gallons per minute). a) Determine the equation of the linear relation (in slope-intercept form) with x = the # of minutes from when the plug was pulled, and y = the # of gallons of water in the bathtub. Sketch the graph. b) What do the slope and the y-intercept of your line indicate? c) Use your equation to determine how much water the bathtub contain 20 minutes after the plug was pulled. d) Use your equation to determine how long after the plug was pulled the bathtub was empty. 4. A pool contained 32 gallons of water thirty minutes after it began to rain. Twenty minutes later (fifty minutes after the rain began to fall), the pool contained 40 gallons of water. Assume it rained at a constant rate (in gallons per minute). a) Determine the equation of the linear relation (in slope-intercept form) with x = the # of minutes it had been raining, and y = the # of gallons of water in pool. Sketch the graph. b) What do the slope and the y-intercept of your line indicate? c) Use your equation to determine how much water the pool will contain two hours after the rain began to fall. d) Use your equation to determine when the pool will overflow (the pool holds up to 100 gallons). 5. Determine the equation of the line through the given pair of points. a) (0, 12) & (2, 15) b) (10, 24) & (15, 21) c) (16, 100) & (24, 140) Supplementary Assignment 4 – Linear Regression NSC/pmkurose 8/2021 Part B: Equations of “Lines of Best Fit” 1. The given scatter plot shows weight versus sprint speed (in feet per second) for the players on a football team. Notice the “breaks” on the axes indicate portions of the graph are not included. a) Do the variables appear to be positively or negatively correlated (explain why)? b) Complete the statement, The more a football player weighs, _______ . c) Determine the equation for the line drawn on the graph. (Use (150, 66) and (250, 52) for the points marked with a +) d) Use your equation to predict the speed for a 180 pound football player. e) Use your equation to predict the weight of a football player who can run 56 feet per second. 2. The given scatter plot shows age versus number of acquaintances (how many people you know). Notice the “breaks” on the axes indicate portions of the graph are not included. a) Do the variables appear to be positively or negatively correlated (explain why)? b) Complete the statement, The older a person is, _______ . c) Determine the equation for the line drawn on the graph. (Use (30, 400) and (50, 560) for the points marked with a +). d) Use your equation to predict the number of acquaintances for a 36 year-old. e) Use your equation to predict the age at which you will know 520 people. 3. The given scatter plot shows x = age versus y = test score data on a test: a) Determine the equation of the approximate line of best fit drawn on the graph. Use (20, 220) and (40, 300) for the coordinates of the points marked on the line with a +: b) What do the slope and the y-intercept of your line indicate? c) Use your equation to predict the test score for a 24 year- old test taker. d) Use your equation to predict the age of someone scoring 260 points on the test. Speed (ft/s) weight 60 250 150 50 70 200 • • • • • • • • • • • • People age 500 50 30 400 600 40 • • • • • • • • • • • • • • • • • • • • • • • • • 40 30 20 200 250 300 Supplementary Assignment 4 – Linear Regression NSC/pmkurose 8/2021 Part C: The Linear Correlation Coefficient 1. a) Give an example of two variables that you believe would be positively correlated. Explain your reasoning. b) Give an example of two variables that you believe would be negatively correlated. Explain your reasoning. 2. a) What does the linear correlation coefficient r = – 0.90 indicate? b) What does the linear correlation coefficient r = 0.35 indicate? 3. For the given scatter-plot: i) state whether the variables appear to be positively correlated, negatively correlated, or to have no correlation; ii) describe the strength of the correlation as weak, moderately weak, moderately strong, or strong; then iii) estimate the value of the linear correlation coefficient. a) b) c) d) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •