Question

Use residuals to determine whether the model is a good fit for the data in the table. Explain. (Make a five sectioned chart)

#1.

y= -0.5x-2
x: 4,6,8,10,12,14,16,18,20
y: -1,-3,-6,-8,-10,-10,-10,-9,-9

Answer 1

for each value of x, calculate the residual.
Then, as I'm sure you know,
Assuming the model you fit to the data is correct, the residuals approximate the random errors. Therefore, if the residuals appear to behave randomly, it suggests that the model fits the data well. However, if the residuals display a systematic pattern, it is a clear sign that the model fits the data poorly.

SO, what do you get, and what do you think it means?

Answer 2

Okay, I understand how the graph should look and the patterns but I’m not sure how to calculate the residuals.

Answer 3

wow - you mean that wasn't the very first thing you thought to check? Surely you weren't assigned to a task involving something you hadn't even studied yet. I hadn't studied this, so I went to google for help on the topic. The very first hit I got on google, which I cited above, started out with the words

The residuals from a fitted model are defined as the differences between the response data and the fit to the response data at each predictor value.

Answer 4

I tried looking on google for how to do it before I asked and I also looked in my math notes from class but the notes just say, step one calculate the residuals. Organize your results in a table. Step 2 use the points (x,residual) to make a scatter plot. I do not understand it. I remember the teacher saying some formula to do it I think but I’m not sure. Oh also, it says that if the points are evenly dispersed about the horizontal axis that the line is a good fit.

Answer 5

the equation of the line is the predictor. So, for x=4,
y= -0.5x-2 = -0.5 * 4 - 2 = -2-2 = -4
The table says y = -1
so the residual is -1-(-4) = 3
That is, the actual response is 3 more than the predicted response for x=4

Now do the same for all the other values