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Do heavier people burn more energy? The exercise10presented data on the lean body mass and resting metabolic rate of 12women 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 per24hour, 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?

Short Answer

Expert verified

(b) The regression line is Y^=197+24.1X.

(c) The rate at which the anticipated response Ymoves among the line as the explanatory variable Xchanges are represented by the slope b of the aforementioned regression line (197).

(d) This indicates that the expected metabolic rate for a lady with a body mass of 45kgis 1281.5calories per 24hours.

(a)

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (a) Step 2: Explanation

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.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

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

The regression line isY^=197+24.1X

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

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

The equation of the least-squares regression line is Y^=197+24.1X

The rate at which the anticipated response Ymoves among the line as the explanatory variable Xchanges is represented by the slope b of the aforementioned regression line (197). bis the expected change in Y when Xis increased by one unit. If mass increases by one unit, metabolic rate increases by 24.1cal/24hrs, as shown in b.

07

Part (d) Step 1: Given information

The given data is

08

Part (d) Step 2: Explanation

The equation of the least-squares regression line, Y^=197+24.1X

For, the predicted value of Yis

Y^=197+24.1X

=197+24.1×45=1281.5

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

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