Question

For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is

predicted tail length =$20+3\times weight$

Which of the following is not correct?

a. The slope is $3$, which indicates that a mouse’s predicted tail length should increase by about $3$mm for each additional gram of weight.

b. The predicted tail length of a mouse that weighs $38$grams is $134$millimeters.

c. By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive.

d. If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been $3/10=0.3$

e. Mice that have a weight of $0$grams will have a tail of length $20$mm.

Short answer

Since we are asked incorrect options, none of these will be the answer as all are correct options.

Step-by-step solution

Part a, Step1: Given Information

We have been that the slope is $3$, which indicates that a mouse’s predicted tail length should increase by about $3$mm for each additional gram of weight.

Part a, Step 2: Explanation

Given,

$predictedtaillength=20+3\times weight$

Hence, slope = $3$.

So, this is correct.

Part b: Step 1: Given Information

We have been that the predicted tail length of a mouse that weighs $38$grams is $134$millimeters.

Part b: Step 2: Explanation

Replacing weight in the given formula with $38g$

$predictedtaillength=(20+3\times 38)mm=134mm$

So, this is correct.

Part c: Step 1: Given Information

We have been that by looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive.

Part c: Step 2: Explanation

This is correct option.

Part d: Step 1: Given Information 

We have been that if you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been $3/10=0.3$.

Part d: Step 2: Explanation

Since, $10mm=1cm$

So, role="math" localid="1653808608556" $$\begin{gathered} 1mm=1/10cm \\ 3mm=3/10cm=0.3cm \end{gathered}$$

Thus, this is the correct option.

Part e: Step 1: Given Information

We have been that mice that have a weight of $0$grams will have a tail of length $20$mm.

Part e: Step 2: Explanation

Replacing weight in the given formula with $0g$.

$predictedtaillength=(20+3\times 0)mm=20mm$

So, this is correct option.