Since the average of the residuals of the model is far from 0, the model is not a good fit for the data in the table.
<h3>What is a residual, and how to verify if a model is a good fit?</h3>
A residual is given by the difference between the observed value, in a table or in a scatter plot, and the predicted value using the line of best fit.
If the average of the residuals in a model is close to 0, the line of best fit is a good fit for the data.
For this problem, the residuals are calculated as follows:
- x = -4: Observed: -18, predicted -21, residual 3.
- x = -3: Observed: -13, predicted -17, residual 4.
- x = -2: Observed: -10, predicted -13, residual 3.
- x = -1: Observed: -7, predicted -9, residual 2.
- x = 0: Observed: -2, predicted -5, residual 3.
- x = 1: Observed: 0, predicted -1, residual 1.
- x = 2: Observed: 6, predicted 3, residual 3.
- x = 3: Observed: 10, predicted 7, residual 3.
- x = 4: Observed: 15, predicted 11, residual 4.
Hence the 9 residuals are given as follows:
3, 4, 3, 2, 3, 1, 3, 3, 4.
Hence the mean is:
M = (3 + 4 + 3 + 2 + 3 + 1 + 3 + 3 + 4)/9 = 2.9.
2.9 is not close to 0, hence the model is not a good fit for the data in the table.
More can be learned about residuals at brainly.com/question/17073231
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