Question

question 12 (1 point)(05.06 lc)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:|enrollment|month| | | | | || ---- | ---- | ---- | ---- | ---- | ---- | ---- || |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|analyze the data. determine whether the equation that produced the predicted values represents a good line of best fit.a no, the equation is not a good fit because the sum of the residuals is a large number.b no, the equation is not a good fit because the residuals are all far from zero.c yes, the equation is a good fit because the residuals are not all far from zero.d yes, the equation is a good fit because the sum of the residuals is a small number.

Explanation:

Step1: Calculate sum of residuals

$90 + (-50) + (-100) + (-100) + 150 + (-50) = 90 - 50 - 100 - 100 + 150 - 50 = 0$

Step2: Evaluate residual magnitude

Residuals: $90, -50, -100, -100, 150, -50$. All are far from 0.

Step3: Evaluate line of fit quality

A good fit has residuals close to 0, not just small sum.

Answer:

b. No, the equation is not a good fit because the residuals are all far from zero.