Question

The table below shows the relationship between the diameter, x, in inches, and the height, y, in feet, of trees in a national park

8.3
10.5
12.9
16.3 77
17.3 81
17980
81
The two models shown were developed to represent the data
Model 1: y
= 1.04r + 61.92
Model 2: y
= 1.212 + 58.4
Create a residual plot for each model and select the true statement based on the residuals for each model

Answer 1

I think the answer is A.

Explanation:

After graphing it in Desmos, I decided model A was better, and that it was non-random.

Answer 2

The correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.

Explanation:

Consider the provided data.

The table shows the relationship between the diameter, x, in inches, and the height, y, in feet, of trees in a national park.

The residual plot for the table is shown in figure 1:

Now, consider the model 1: y = 1.04 x + 61.92

The residual of the above model is shown in figure 2:

Consider the model 1: y = 1.21 x + 58.4

The residual of the above model is shown in figure 3:

Now observe the figure 4 which compare all the three residuals.

By comparing the residual of all the three models it can be concluded that 'Model 2 has a random pattern and is a good fit for the data.

Therefore, the correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.