Question

name: alg1_fsq01_u5a - u3_pb_fy26 id: 3690182 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. exercise and weight loss residual, 0 hours of exercise, (x, in hours) which conclusion about the fit of the function is supported by the residual plot? a the function is an appropriate fit and represents a negative, linear association between hours of exercise and weight loss. b the function is an appropriate fit and represents a positive, linear association between hours of exercise and weight loss. c the function is an inappropriate fit of the association between hours of exercise and weight loss. d there is no association between hours of exercise and weight loss.

Explanation:

In a residual plot, if the points are randomly scattered around the horizontal axis (residual = 0), the function is a good fit. Here, the points are randomly scattered, indicating a good fit. The function $y = 3+0.5x$ has a positive slope (0.5), so it represents a positive linear association between hours of exercise ($x$) and weight - loss ($y$).

Answer:

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