Melissa collected the data in the table.
| x | Given | Predicted | Residual |
|---|---|---|---|
| 1 | 2 | 1 | 1 |
| 2 | 3 | 4 | -1 |
| 3 | 8 | 7 | 1 |
| 4 | 9 | 10 | ? |
When x=4, what is the residual?
A. -3
B. -1
C. 1
D. 3
Answer (2)
The residual when x = 4 is calculated as 9 − 10 = − 1 . Therefore, the correct answer is B. -1.
;
The problem provides 'Given' and 'Predicted' values and asks for the 'Residual' when x = 4 .
The residual is calculated using the formula: Residual = Given − Predicted .
Substitute the values: Residual = 9 − 10 .
Calculate the residual: − 1 .
Explanation
Understanding the Problem We are given a table with values for 'Given' and 'Predicted' at different values of x . The 'Residual' is defined as the difference between the 'Given' and 'Predicted' values. Our goal is to find the residual when x = 4 .
Identifying the Formula and Values The formula for calculating the residual is: Residual = Given − Predicted When x = 4 , we have: Given = 9 Predicted = 10
Substituting the Values Substitute the given values into the formula: Residual = 9 − 10
Calculating the Residual Calculate the residual: Residual = − 1
Final Answer Therefore, when x = 4 , the residual is − 1 .
Examples
In data analysis, residuals help us understand how well a model fits the data. For instance, if you're predicting house prices based on size, the residual is the difference between the actual price and the predicted price. A small residual means the model is a good fit, while a large residual indicates the model isn't accurately predicting the price. By analyzing residuals, we can improve our models and make better predictions.
