Chapter 3.2, Problem 54E

(a)

To determine

To make: a scatterplot for the given data

Answer to Problem 54E

Explanation of Solution

Given:

Mass:	36.1	54.6	48.5	42.0	50.6	42.0	40.3	33.1	42.4	34.5	51.1	41.2
Rate:	995	1425	1396	1418	1502	1256	1189	913	1124	1052	1347	1204

Calculation:

We put mass (the explanatory variable) on the horizontal axis and metabolic rate (the response variable) on the vertical axis.

The below figure is the completed scatterplot for the given data.

Conclusion:

Thus, the required scatterplot is drawn.

(b)

To determine

To find: the equation of the least-squares regression line.

Answer to Problem 54E

The regression line is $\widehat{Y}=197+24.1X$

Explanation of Solution

Calculation:

Using the MINITAB, the equation of the least-squares regression line is,

  

The regression line is $\widehat{Y}=197+24.1X$

Observe the above scatter plot the data with regression line added.

Conclusion:

Therefore, the regression line is $\widehat{Y}=197+24.1X$

(c)

To determine

To explain: the slope of the regression line

Answer to Problem 54E

Here the slope b of above regression line (197) is the rate at which the predicted response Y changes among the line as the explanatory variable X changes.

Explanation of Solution

The equation of the least-squares regression line,$\widehat{Y}=197+24.1X$

Here the slope b of above regression line (197) is the rate at which the predicted response Y changes among the line as the explanatory variable X changes. Specifically, b is the predicted change in Y when X increases by 1 unit. Here b shows if mass increases by 1 unit then metabolic rate increases by 24.1 cal/24 hrs.

(d)

To determine

To find: the predicted metabolic rate of the woman

Answer to Problem 54E

The predicted metabolic rate for woman of body mass 45 kg is $\text{1281}\text{.5 cal/24 hrs}$

Explanation of Solution

Given:

Woman has a lean body mass of 45 kilograms

Calculation:

The equation of the least-squares regression line,$\widehat{Y}=197+24.1X$

For $X=45$ kg, predicted value of Y is.

  $\begin{array}{c}\widehat{Y}=197+24.1X\\ =197+24.1\times 45\\ =1281.5\end{array}$

This shows that predicted metabolic rate for woman of body mass 45 kg is $\text{1281}\text{.5 cal/24 hrs}$

Conclusion:

Therefore, the predicted metabolic rate for woman of body mass 45 kg is $\text{1281}\text{.5 cal/24 hrs}$