A team of archeologists have discovered the fossil skull of an extinct and exceptionally large crocodile (sarcosuchus). Unfortunately, they have not been able to find any bones other than the skull, and, therefore, are not able to determine the length of the body of this extinct species. The snout of a crocodile which is alive and well in Northern Australia (crocodylus porosus) closely resembles that of the extinct crocodile (sarcosuchus), the crocodylus porosus may be used to estimate the body length of sarcosuchus. Body measurements for the crocodylus porosus were collected and measured in Northern Australia. The data are available in the file crocodylusporosus.xls Attached with this exam. The data represent the head length and total body length of several crocodylus porosus. In this activity, you will use this data to find a regression line which relates head length to total body length and then use this regression line to predict the total body length (in centimeters) of the extinct crocodile from the head length measured from the fossil skull (in centimeters).
Descriptive Statistics
a) Determine the explanatory variable and response variable.
b) Create a scatterplot using SPSS and include the regression line on the plot.
c) Calculate the correlation between head length and body length.
d) Determine the form, strength and direction of the relationship based on the first three steps.
e) Find the least square regression equation for this relationship.
f) If the head length of sarcosuchus is 160 cm, what is the predicted body length of sarcosuchus? (Please ignore that we are extrapolating)
Diagnostics
g) Calculate R^{2}
h) Look at the histogram and normal probability plots for the residuals. When checking these plots, what pattern(s) do you see that might concern you?
i) Would you conclude that the assumption holds that that the residuals are normally distributed? Explain. (2 pts).
Inferential Statistics
j) Can you conclude that there is a linear relationship between head length and total body length in this type of crocodile? Write out all of the details for the hypothesis test which answers this question.
k) Write out the details for the hypothesis tests to determine if the constant and slope of the Regression Line are meaningful. Make sure to give your conclusions in both statistical jargon and regular English.
l) Using the confidence intervals for the constant and slope of the regression line determine the smallest and largest total body lengths you would predict for the extinct crocodile (head length of 160 cm).
m) On average, one centimeter of head length growth corresponds to how many centimeters of total body length growth in this type of crocodile?