The theater director recorded the number of seats occupied at past performances and the total revenue per
performance.
After plotting her results, the director noticed that the relationship between the two variables was fairly linear,
so she used the data to calculate the following least squares regression equation for predicting the total
revenue, in dollars, from the number of seats occupied.
= -325 + 143
What is the residual of a performance with a revenue of $700 and 70 seats occupied ?

$45 (with the assumption made below)

Step-by-step explanation:

The equation is garbled; thus, to explain you I will assume the equation is

R(s) = -325 + 14s

Where:

R(s) is the revenue in dollars, as a function of the number of seats occupied.s is the variable that represents the number of seast occupied14 is the rate of change of the revenue per seat occupied (the price of a ticket).-325 is the fixed cost of the theater for a performance (the amount of money the theater will lose if none seat is occupied).

Thus, you can predict the revenue when 70 seats are occupied by substituting s with 70.

R(70) = -325 + 14(70)R(70) = -325 + 980 = $655

The residual value from a prediction is equal to the real value (observed value) less the preducted value:

Residual = real revenue - predicted revenueResidual = $700 - $655 = $45

You would plot 83 on the 83 line and you would plot -113 on the -113 line.