Question

100 PONITS PLEASE ANSWER

A-D
A person's lean body mass measures how much non-fat mass a person has.
This includes bones, muscles and organs. A person's metabolic rate is how nuch energy a body burns while at rest. Below are the body mass and netabolic rates for 12 people.

a. Create a scatter plot for the body masses and metabolic rates.

b. Calculate the correlation coefficient.

c. Use the scatter pot and the correlation coefficient to explain if there is a correlation between body mass and metabolie rate.

d. Will a person's body mass go up if their metabolic rate goes up? Explain your answer.

Answer 1

(a) See attachment.

(b) r = 0.8765 (4 d.p.)

(c) Strong positive correlation.

(d) See explanation.

Explanation:

Part (a)

Correlation measures how closely two variables are linked.

When creating a scatter plot with bivariate data:

• The explanatory (independent) variable is drawn on the x-axis.
• The response (dependent) variable is drawn on the y-axis.

Plot a scatter diagram using the data from the given table and the following variables.

• Explanatory variable = Body mass (in kg).
• Response variable = Metabolic rate (cal/day).

(See attachment).

Part (b)

The correlation coefficient (r) measures the strength of the linear correlation between two variables.

Using a calculator and the given data, calculate r:

• r = 0.8765 (4 d.p.).

Part (c)

As r is close to +1, this suggests that the data has a strong positive correlation.

This suggests that the metabolic rate increases as the body mass increases.

Part (d)

We cannot use a regression line to predict a value of the explanatory variable. Therefore, as the body mass is the explanatory variable, we cannot say that a person's body mass will increase if their metabolic rate increases. However, we can say that according to the scatter plot and correlation coefficient, it is highly likely that a person's metabolic rate increases as their body mass increases.

Remember to apply caution when using values of of x outside the range of the original data to predict corresponding values of y, as these predications can be unreliable since there is no evidence that the relationship is true for all values of x.