Question

a new weight loss medication is in clinical trials. a scientist wants to analyze the drugs effectiveness when combined with exercise. he gathers data from 18 subjects and creates a scatter plot comparing their weight loss over a six month period to their average weekly exercise. which of the following statements are true about the line of best fit that the scientist plans to add to the plot? i. a y - value of zero represents weight lost with no exercise. ii. the relationship between hours exercised and weight lost is decreasing linear. iii. an x - value of zero represents weight lost with no exercise. iv. the slope represents the amount of weight lost for each hour of exercise. a i, ii b i, iv c ii, iii d iii, iv

Explanation:

Step1: Analyze statement I

A \( y \)-value of zero would mean no weight loss. But the \( x \)-axis is hours exercised. So, this statement is incorrect.

Step2: Analyze statement II

Looking at the scatter - plot, as \( x \) (hours exercised) increases, \( y \) (weight loss) generally increases. So, the relationship is increasing linear, not decreasing linear. This statement is incorrect.

Step3: Analyze statement III

The \( x \)-axis is labeled "Hours Exercised per Week". An \( x \)-value of zero means no exercise. So, this statement is correct.

Step4: Analyze statement IV

In a linear regression model \( y=mx + b\) (where \(y\) is weight loss and \(x\) is hours of exercise), the slope \(m\) represents the change in \(y\) (weight loss) for a unit change in \(x\) (hours of exercise). So, this statement is correct.

Answer:

D. III, IV