Chapter 3.2, Problem 61E

To determine

To explain: whether it is correct to use the regression line to predict y from x

Answer to Problem 61E

A straight line is not an appropriate model for these data.

Explanation of Solution

Given:

  $\stackrel{⌢}{\text{weight}}=4.88+0.267\left(\text{age}\right)$

Age (months):	1	2	3	4	5	6	7	8	9	10	11	12
Weight (kg):	4.3	5.1	5.7	6.3	6.8	7.1	7.2	7.2	7.2	7.2	7.5	7.8

Calculation:

A hasty user of statistics enters the data into software and computes the least square line without plotting the data.

The result is $\stackrel{⌢}{\text{weight}}=4.88+\mathrm{0.2670.05762}\left(\text{age}\right)$

The displayed residual plot in effect turns the regression line horizontal. It magnifies the deviations of the points from the line, if the regression line captures the overall pattern of the data, there should be no pattern in the residuals. The above figure shows a residual plot with a clear curved pattern. A straight line is not an appropriate model for these data.