Question

question 1 (multiple - choice worth 1 points)
(04.15 lc)
an equation was created for the line of best fit from the actual enrollment data. it was used to predict the dance studio enrollment values shown in the table below.
analyze the data. determine whether the equation that produced the predicted values represents a good line of best fit.

Explanation:

Step1: Recall the concept of residuals

Residual = Actual - Predicted. A good - fit line should have residuals that are randomly distributed around zero. The sum of residuals can be used as a rough measure (although in more advanced statistics, sum - of - squared residuals is more commonly used for goodness - of - fit in simple linear regression).

Step2: Calculate the sum of residuals

Sum of residuals \(=4+( - 1)+( - 1)+1+( - 1)+( - 1)=1\). A small sum of residuals (close to zero) indicates that the line is a relatively good fit. If the sum of residuals is large (in magnitude), it means that, on average, the predicted values are far from the actual values. Also, if residuals are all far from zero (either positive or negative), the line is not a good fit.

Answer:

C. The equation is a good fit because the sum of the residuals is a small number.