We are interested in exploring the relationship between the weight of a vehicle and its fuel effi- ciency (gasoline mileage). The data in the table show the weights, in pounds, and fuel efficiency, measured in miles per gallon, for a sample of 12 vehicles.
a. Graph a scatterplot of the data.
b. Find the correlation coefficient and determine if it is significant.
c. Find the equation of the best fit line.
d. Write the sentence that interprets the meaning of the slope of the line in the context of the data.
e. What percent of the variation in fuel efficiency is explained by the variation in the weight of the vehicles, using the regression line? (State your answer in a complete sentence in the context of the data.)
f. Accurately graph the best fit line on your scatterplot.
g. For the vehicle that weights 3000 pounds, find the residual (y-yhat). Does the value predicted by the line underestimate or overestimate the observed data value?
h. Identify any outliers, using either the graphical or numerical procedure demonstrated in the textbook.
i. The outlier is a hybrid car that runs on gasoline and electric technology, but all other vehicles in the sample have engines that use gasoline only. Explain why it would be appropriate to remove the outlier from the data in this situation. Remove the outlier from the sample data. Find the new correlation coefficient, coefficient of determination, and best fit line.
j. Compare the correlation coefficients and coefficients of determination before and after removing the outlier, and explain in complete sentences what these numbers indicate about how the model has changed.