Quiz-9

Short answer solutions

Question: The prepare readings for Monday (Chapter 7) fit the following line of best to predict possums’ head length, explained by the total length of the possum.

\(\hat{y} = 41 + 0.59x\)

Interpret 0.59 in the context of the possum problem. That means use the variable names, and not just say x and y.

Answer: For a 1 cm increase in total possum length, we estimate the mean head length of a possum to increase by 0.59 mm.

Question: The prepare readings for Monday (Chapter 7) fit the following line of best to predict possums’ head length, explained by the total length of the possum.

\(\hat{y} = 41 + 0.59x\)

Question: The prepare readings for Monday (Chapter 7) fit the following line of best to predict possums’ head length, explained by the total length of the possum.

\(\hat{y} = 41 + 0.59x\)

In detail, explain (using the equation found of the following slide) how this line was chosen over any other potential line to explain the relationship between possum total length and head length.

Answer This line is considered the “line of best fit” because it is the line that fits our data the best. That is, this is the line that minimizes the residual sums of squares (i.e. minimizes the distance that all points are away from a given line).