7. Here are data for 12 perch caught in a lake in Finland:
Weight Length Weight Length
(grams) (cm) (grams) (cm)
5.9 8.8 300.0 28.7
100.0 19.2 300.0 30.1
110.0 22.5 685.0 39.0
120.0 23.5 650.0 41.4
150.0 24.0 820.0 42.5
145.0 25.5 1000.0 46.6
(a) Suppose you want to use the length of a perch to predict its weight. Use your calculator to make an appropriate scatterplot. Describe what you see.
(b) How do you expect the weight of animals of the same species to change as their length increases? Make a transformation of weight without using logarithms that should straighten the plot if your expectation is correct. Plot the transformed weights against length. Then find the equation of the least-squares line for the transformed data. Record the equation below. Define any variables you use.
(c) How well does the linear model you calculated in (b) fit the transformed data? Justify your answer with graphical and numerical evidence.
(d) Use your model from (b) to predict the weight of a Finnish perch whose length is 35 cm. Show your method.
Thank you so much!