Question

question 1-6
petra is a personal trainer at a gym and wants to track the weight loss of 10 clients over a 4 - week period. she records the number of hours, x, they exercise each week and their weight loss, y, in pounds. she models the data with the function y = 3+0.5x. to analyze the fit of the function, petra creates the residual plot below.
which conclusion about the fit of the function is supported by the residual plot?
the function is an appropriate fit and represents a negative, linear association between hours of exercise and weight loss.
the function is an appropriate fit and represents a positive, linear association between hours of exercise and weight loss.
the function is an inappropriate fit of the association between hours of exercise and weight loss.
there is no association between hours of exercise and weight loss.

Explanation:

Step1: Recall residual - plot rules

If the points in a residual plot are randomly scattered around the horizontal axis, the function is a good fit for the data.

Step2: Analyze the given residual plot

The points in the given residual plot are randomly scattered around the horizontal axis ($y = 0$). So the function $y=3 + 0.5x$ is a good fit.

Step3: Determine the association type

The slope of the function $y = 3+0.5x$ is $m = 0.5>0$. A positive - slope indicates a positive linear association between $x$ (hours of exercise) and $y$ (weight loss).

Answer:

The function is an appropriate fit and represents a positive, linear association between hours of exercise and weight loss.