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Regression Video Lecture Sections 3 4 4 1 5 9 Course Learning Objectives Graph functions and use such graphs to solve applied problems and to understand the significance of attributes of the graph to such applied problems Weekly Learning Objectives 1 Use tables on a graphing utility 2 Use a graphing utility to create a scatterplot from data 3 Use a graphing utility to find and plot a regression line 4 Use a graphing utility to find regression curves Regression Pressure at Various Ocean Depths Depth ft 5 8 12 15 18 22 25 30 Pressure lb in 15 5 20 3 20 7 20 8 23 2 23 8 24 9 29 3 1 Make a scatterplot of the data 2 Find the Regression Line 3 Plot the linear regression on top of the scatterplot to see the fit Asbestos Exposure Versus Percent of Rats That Develop Lung Tumors Asbestos Exposure fibers mL 50 400 500 900 1100 1600 1800 2000 3000 that develop lung tumors 2 6 5 10 26 42 37 28 50 1 Make a scatterplot of the data 2 Find the Regression Line 3 Plot the linear regression on top of the scatterplot to see the fit Femur Length and Height Fenur Length cm 50 1 48 3 45 2 44 7 44 5 42 7 39 5 38 0 Height cm 178 5 173 6 164 8 163 7 168 3 165 0 155 4 155 8 1 Make a scatterplot of the data 2 Find the Regression Line 3 Plot the linear regression on top of the scatterplot to see the fit 4 An anthropologist finds a femur length of 58 cm How tall was the person David is conducting an experiment to estimate the acceleration of an object due to gravity He takes a ball and drops it from different heights and records the time it takes for the ball to hit the ground using an optic laser connected to a stop watch He collects the following data a Time seconds Distance feet 1 003 16 1 365 30 1 769 50 2 093 70 2 238 80 Draw a scatter plot using time as the independent variable and distance as the dependent variable b Find a power function of best fit to the data c Graph the data points and the power function of best fit d Predict how long it will take an object to fall feet e Physics theory states that the distance that an object falls is directly proportional to the time squared Rewrite the model found in part b so that it is of the form 1 where is distance 1 is the acceleration due to gravity and is time What is David s estimate of the acceleration of gravity A chemist has a gram sample of a radioactive material He records the amount of radioactive material every week for 6 weeks and obtains the following data Week 0 1 2 3 4 5 6 Weight in grams 100 0 88 3 75 9 69 4 59 1 51 8 45 5 a Draw a scatter plot with week as the independent variable b Find the equation of an exponential curve to the data in the form of E E 5 c Graph the scatter plot and the equation of the curve of best fit d Determine the half life of the material e How much radioactive material will be left after 1 year