15000 2000 12000 5 10 15 20 25 30 36 40 45 50 miles Model 2: log i = 4.4901-.0071910x 40.9765 Log(price) vs. miles Residuals 0.05 45 0:04 4 45 0.03 4 4- 0.02 4 36 0 01 43 4 25 0.01 42 0.02 4 15 -0 03 0.04 5 10 15 20 25 30 35 40 45 50 Model 3: - 43254-17153 log x r=-0.9975 Price vs. log(miles) Residuals 32000 600 400 10000 200 200 400 600 -800 -1000 02 04 06 08 1 12 14 16 18 log(miles)1 The equation y = 54 + 9.1x is used to model the score on a final exam in Chemistry from the amout of time studied in hours for students who studied between 0 and 3 hours (times were recorded in increments of 10 : minutes). The correlation coefficient was found to be r = 0.93. Is it reasonable to conclude the amount of time studied causes the final exam score? Why or why not? 4 The data shown represents the weight in pounds for couches (x) and their sales price in dollars (y). U On the graph, identify a point with high leverage. What will removing this point do to the regression equation? Report the regression equation, correlation coefficient, and coefficient of determination before and after removing the point and discuss the changes in these values. Show Your Work Weight Price 65 450 80 685 125 725 175 790 850 350 2575 450 1553 650 1575 1995 1550 3200Couch Mart recently did inventory and found that all of their couches weigh between 65 and 1550 pounds. B The data shown represents the weight in pounds for the couches and their sales price in dollars. Calculate the linear regression model using your graphing calculator. Report the linear regression equation and interpret the slope and y-intercept in context. Be sure to use appropriate notation. What is the correlation, and what does it tell you about the relationship of these two variables? Weight. Price 65 450 80 685 125 725 175 790 200 850 350 2575 450 1553 650 1575 975 1995 1550 3200 For the problem above, predict the sales price of a couch weighing 45 pounds (if possible). If not possible, state why not. 1 -5 00 For a Honda Civic, the resale price in dollars, y, and the number of miles driven (in thousands of miles), x, were recorded. The model equation, scatterplot, and residual plot are shown for the linear regression model, as well as two transformations. Choose the model that best represents the data and defend your choice. Make a prediction for the resale price of a car with 25,000 miles using your selected model. Find the residual for this point if the car sold for $18,750. Was this point underpredicted or overpredicted? Model 1: = 29784 - 343.58x r=-0.9452 Price vs. miles Residuals 3500 33000 3000 30000 2500 2000 27000 1500 1000 24000 500 21000 500 18000 -1000 15000 -1500 2000 12000 5 10 15 20 25 30 35 40 45 50 2500 Model 2: log i = 4.4901-.0071910x r =-0.9765 Residuals Log(price) vs. miles 0.05 0.04 0.03 0.02 0.01 436 50