a. Produce a scatterplot of gestation vs. longevity Also calculate the correlation coefficient. Comment on what the scatterplot and correlation coefficient reveal.
b. Use your calculator to determine the least squares line for predicting an animal's gestation period from its longevity. Report its equation and the value of r^2.
c. Use the least squares line to calculate the fitted value and residual for a baboon. Hint: First, find the baboon's longevity and gestation period in the data table.
d. Use your calculator to create a residual plot of the animals' residual value vs. longevity. Is there any relationship between residuals and longevities? Explain in a sentence or two what this relationship signifies about the accuracy of predictions for animals with long vs. short lifetimes.
e. Which animal is clearly an outlier both in longevity and in gestation period? Determine its residual value. Does it have the greatest residual (in absolute value) of any animal?
f. Which animal has the greatest (in absolute value) residual? Is its gestation period longer or shorter than expected for an animal with its longevity?
g. Remove the giraffe from the analysis. Reproduce the scatterplot and determine the least squares line with the giraffe omitted. Report the equation of the line and value of r^2. Have these changed considerably from the original analysis that included the giraffe in the dataset?
h. Return the giraffe's values to the analysis, and then remove the elephant. Again reproduce the scatterplot and determine the least squares line with the elephant omitted. Have these changed considerably from the original analysis?
i. In which case (giraffe or elephant), did the removal of one animal affect the regression line more? In other words, which animal has more influence on the least squares line?
j. Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years. Show the details of your calculation.
k. Do you accept this prediction from part (j) as being reasonable? If not, explain why the least squares line does not produce a reasonable prediction in this case.