Question

The number of hours slept at night is related to the number of minutes spent exercising that day. A collection of data on the number of minutes spent exercising, x, and the number of hours slept, y, is shown in the table below.

x y
30 6.25
37 6
40 6.5
45 7
52 6.5
55 7.25
61 7.5
65 8
71 8.65
76 8.5

Using a residual plot, determine if the following model is a good fit for the data in the table above.

The model is for the data in the table because the residual plot has a pattern of data points about the horizontal axis.

Answer 1

hm. this is a pain to do by hand, but you could plug your data points into a residual plot maker like desmos

https://www.desmos.com/calculator/vkp6wlqjhj

then, you would see if the residual plot has an obvious pattern, like being linear or a parabola or something. if there's an obvious pattern, the model is poor; otherwise it is a good model