6. Use the following to answer questions a-d: A biologist collected data on a sa

Question

6. Use the following to answer questions a-d:

A biologist collected data on a sample of 20 porcupines. She wants to be able to predict the body mass of a porcupine (in grams) based on the length of the porcupine (in cm). Her least squares regression equation is m= -3089 +175.6Length , where M is the mass.

        a. Interpret the slope of the least squares regression line, in the context of the situation.

        b. If it would make sense, provide a clear interpretation of the intercept of the regression line, in context. Otherwise, explain why the interpretation does not make sense.

        c. Predict the body mass of a porcupine that is 51 cm long. Report your answer using one decimal place.

            d.       One of the porcupines in the dataset had a body length of 51 cm and a body mass of 5,281 g. Calculate the residual for this porcupine. Use one decimal place in your calculation.

Explanation / Answer

a) Here the regression equation given is:

M = -3089 +175.6*Length

The slope of the regression equation here is 175.6 where the interpretation of the slope here is that for every unit increase in the length there would be an increase in 175.6 units in mass.

b) As the intercept here is negative, and we know that mass cannot be negative, we cannot have any clear interpretation of intercept here because the intercept is interpreted as the value of mass for which the length is 0.

c) Here the mass is computed using the length of 51 cm as:

M = -3089 +175.6*Length = -3089 +175.6*51 = 5866.6 grams

Therefore 5866.6 grams is the predicted mass here.

d) The residual is computed as:

Residual = Observed value - Predicted value = 5281 - 5866.6 = -585.6

Therefore -585.6 is the residual value here.

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