This exercise relates to the data set given in problem number 21 of section 4.2 on pages 217. Answer the following questions based on the data given below. Do not answer the questions in the book.
Least squares regression line: y = -0.0069x+42.9
Correlation coefficient: r = -0.892
1. If you are using the weight of the car to explain the miles per gallon the car gets, what is the explanatory variable and what is the response variable? Draw a scatter diagram. This does not have to be perfect. Only spend about 5 minutes to get a rough idea of what it looks like.
2. Graph your regression line on your scatter diagram. Label the points used to draw your line.
3. Interpret the slope of your regression line in terms of the variables of the problem.
4. Interpret the y-intercept of your regression line in terms of the variables of the problem. What does this mean? Think about it and come up with a conclusion.
5. Calculate the coefficient of determination and explain its meaning in terms of the variables of the problem.
6. How many mpg does your regression equation predict occur if the weight is 3000 pounds?
7. Would it be reasonable to use the least squares regression line to predict the mpg for a Toyota Prius? Why or why not?