Gas Tank Problem: Lisa Carr fills up her cars gas tank and drives off. This table shows

Chapter 8, Problem 3

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Gas Tank Problem: Lisa Carr fills up her cars gas tank and drives off. This table shows the numbers of gallons of gas left in the tank at various numbers of miles she has driven. a. Run a linear regression on the data. Write down the linear regression equation, and r2 and r. How do these numbers tell you that the regression line fits the data perfectly? Why is r negative? b. Calculate the coefficient of determination and the correlation coefficient again, directly from the definition, by calculating SSdev and SSres. Do the answers agree with part a? c. Plot the data and the regression equation on the same screen. How can you tell graphically that the regression line fits the data perfectly? d. According to your mathematical model, how much gas does the gas tank hold? How many miles per gallon does Lisas car get? e. Show that your mathematical model predicts that the tank is empty after 340 miles. Because this number is found by extrapolation, how confident are you that the car will actually run out of gas after 340 miles?