Question

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:
Enrollment Month
January February March April May June
Actual 500 400 550 13 16 14
Predicted 8 15 15 12 17 15
Residual 4 −1 −1 1 −1 −1
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 all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.

Answer 1

Answer:  First option is correct.

Step-by-step explanation:

Enrollment month   Actual   Predicted   Residual

January                   500           8                4

February                 400           15              -1

March                     550            15              -1

April                         13              12              -1

May                         16              17              -1

June                        14              15              -1

Since we know that

Residual value = Actual value - Predicted value

Sum of residuals is given by

$4-1-1+1-1-1=1$

since we can see that sum of residual is more than 0.

So, it can't be a good fit .

Hence, No, the equation is not a good fit because the sum of the residuals is a large number.

Therefore, First option is correct.