MATH&146 Introduction to Statistics Linear Regression Worksheets I and II Linear
ID: 3309850 • Letter: M
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MATH&146 Introduction to Statistics Linear Regression Worksheets I and II Linear R Part I: Linear Function Review 1. a) A tree was 12 tall when it was planted. After 3 weeks, the tree was 16" tall. Determine the average rate at egression Worksheet I which the tree grew in inches per week (to the nearest hundredth of an inch per week) Aman 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) Atage 10, Mason was 130 centim eters tall. At 16, he was 175 centimeters tall. Determine Mason's average growth rate from age 10 to 16 in centimeters per year (to the nearest tenth of a centimeter per year) b) c) 2. Write an equation for the deseribed linear relation Kenji started with $50 in his bank account, then deposited $10 per week. Let of neeks and y account balance 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 Asnowball 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 a) b) c) 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 = the # of minutes from when b) c) d) the plug was pulled, and y = the # of gallons of water in the bathtub. Sketch the graph. What do the slope and the y-intercept of your line indicate? Use your equation to determine how much water the bathtub contain 20 minutes after the plug was pulled 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 a) Determine the equation of the linear relation (in slope-intercept form) with = the # of minutes it had been b) c) d) raining. and y = the # of gallons of water in pool. Sketch the raph. What do the slope and the y-intercept of your line indicate? Use your equation to determine how much water the pool will contain two hours after the rain began to fall Use your equation to determine when the pool will overflow (the pool holds up to 100 gallons) Part : Equations of "Lines of Best Fit', 5. 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)? Complete the statement, The more a football player weighs 70 b) 60 c) Determine the equation for the line drawn on the graph. (Use the points marked with a +) Use your equation to prediet the speed for a 120 pound football player Use your equation to predict the weight of a football player Speed 50 d) e) who can run 40 feet per second 150 200 250 weightExplanation / Answer
1a)
The tree grow by 16- 12 = 4 " in three weeks. So the average rate of growth per week is
4 / 3 = 1.33 "
b)
The change in weight in 6 months is 200 -180 =20 pounds. That is person loses 20 pounds in 6 months. So average rate of weight loss per month is
20 /6 = 3.3 pounds per month
c)
Change in height in 6 years is 175 - 130 = 45
So the average growth rate per year is
45 /6 = 7.5 centimeters per year
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