Do heavier people burn more energy? The exercise$10$presented data on the lean body mass and resting metabolic rate of $12$women who were subjects in a study of dieting. Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate, in calories burned per$24$hour, is the rate at which the body consumes energy. Here are the data again.

(a) Enter the data into your calculator and make a scatterplot.

(b) Use your calculator’s regression function to find the equation of the least-squares regression line. Add this line to your scatterplot from (a).

(c) Explain in words what the slope of the regression line tells us.

(d) Another woman has a lean body mass of $45-$kilograms. What is her predicted metabolic rate?

The given data is

From the given data

On the horizontal axis, we plotted mass (the explanatory variable) and metabolic rate (the response variable).

The finished scatterplot for the given data is shown below.

The given data is

The least-squares regression line's equation using the MINITAB is,

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

Look at the scatter figure above with the regression line added.

The given data is

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

The rate at which the anticipated response $Y$moves among the line as the explanatory variable $X$changes is represented by the slope b of the aforementioned regression line $\left(197\right)$. $b$is the expected change in Y when $X$is increased by one unit. If mass increases by one unit, metabolic rate increases by $24.1cal/24hrs$, as shown in $b$.

The given data is

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

For, the predicted value of $Y$is

$\hat{Y}=197+24.1X$

$$\begin{gathered} =197+24.1\times 45 \\ =1281.5 \end{gathered}$$

This indicates that the expected metabolic rate for a lady with a body mass of $45kg$is $1281.5$calories per $24$hours.