A residual compares an actual result with the value predicted by a best-fit model. First convert the input into the units the model uses, then evaluate the given line in Desmos. Subtract actual minus predicted, and use the sign to tell which count was larger. Reversing the subtraction gives the right gap with the wrong sign.
Hints
- Hint 1
The model measures ad spending in hundreds of dollars. How many hundreds are in the week’s ad budget? The dollar amount itself isn’t the value to substitute for .
- Hint 2
A prediction comes from the line, not from the actual order count. Evaluate the given line at your converted input to find how many orders it predicts.
- Hint 3
A residual is actual minus predicted. If the actual count is smaller than the prediction, should that subtraction be positive or negative?
Step-by-step
Evaluate the model, then find the residual
Step 1Convert the spending to the model’s units
Because counts hundreds of dollars, convert the $800 spent on ads to hundreds:
Use for , not . The model’s input is hundreds of dollars, not dollars.
- Step 2
Find the predicted number of orders
The given line is a model: it predicts orders from spending. Type in Desmos, then type . Desmos shows , so the predicted number of orders is . The orders the company received are the actual count, not the prediction.
- Step 3
Subtract and interpret the sign
Use the given residual rule, actual minus predicted. Type below the earlier Desmos lines:
Desmos shows . The negative sign means the actual count was lower, so the line predicted more orders than were placed. Choice A.