Regression Video LectureSections 3.4, 4.1, 5.9Course 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.RegressionPressure at Various Ocean DepthsDepth (ft) Pressure (lb/in )5 15.58 20.312 20.715 20.818 23.222 23.825 24.930 29.3$1) Make a scatterplot of the data2) Find the Regression Line.3) Plot the linear regression on top of the scatterplot to see the fit.Asbestos Exposure Versus Percent of RatsThat Develop Lung TumorsAsbestos Exposure (fibers/mL) % that develop lung tumors50 2400 6500 5900 101100 261600 421800 372000 283000 501) Make a scatterplot of the data2) Find the Regression Line.3) Plot the linear regression on top of the scatterplot to see the fit.Femur Length and HeightFenur Length (cm) Height (cm)50.1 178.548.3 173.645.2 164.844.7 163.744.5 168.342.7 165.039.5 155.438.0 155.81) Make a scatterplot of the data2) 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 theperson?David is conducting an experiment to estimate the acceleration of anobject due to gravity. He takes a ball and drops it from differentheights and records the time it takes for the ball to hit the ground usingan optic laser connected to a stop watch. He collects the followingdata. Time (seconds) Distance (feet)1.003 161.365 301.769 502.093 702.238 80 a) 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 isdirectly proportional to the time squared. Rewrite the modelfound in part b) so that it is of the form , where is= œ 1> ="##distance, is the acceleration due to gravity, and is time.1 >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 for6 weeks and obtains the following data. Week Weight (in grams)0 100.01 88.32 75.93 69.44 59.15 51.86 45.5a) Draw a scatter plot with week as the independent variable. b) Find the equation of an exponential curve to the data in theform of E > œ 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