An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
January February March April May June
Actual 500 400 550 550 750 400
Predicted 410 450 650 650 600 450
Residual 90 −50 −100 −100 150 −50
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Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
Obviously, how good of a fit an equation is just by looking at its error over as few as 5 entries does not give us enough information to answer the question with certainty. However, given that you are measuring something as complex as enrollment data, to me it seems like your residuals are fine. It is up to you to decide whether this is a good estimation.
So if you agree with my judgment, go for "Yes, the equation is a good fit because the residuals are not all far from zero."
If you disagree with my judgment, go for " No, the equation is not a good fit because the residuals are all far from zero."
In no case would you go for the other two, as the first and fourth option forget to take into account that you have to average the errors, not just sum them up.