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 is calculated as Given - Predicted.
When x=4, Given = 9 and Predicted = 10.
Calculate the residual: 9 - 10 = -1.
The residual when x=4 is − 1 .
Explanation
Understanding the Problem We are given a table with values for x , 'Given', 'Predicted', and 'Residual'. We need to find the residual when x = 4 . The residual is calculated as the difference between the 'Given' value and the 'Predicted' value.
Setting up the Calculation When x = 4 , the 'Given' value is 9 and the 'Predicted' value is 10. To find the residual, we subtract the 'Predicted' value from the 'Given' value:
Calculating the Residual Residual = Given - Predicted = 9 - 10 = -1
Final Answer Therefore, the residual when x = 4 is -1.
Examples
In data analysis, residuals help us understand how well a model fits the data. For example, 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 very accurate for that particular house. By analyzing residuals, we can improve our models and make better predictions.
The residual when x=4 is calculated as the difference between the Given value (9) and the Predicted value (10), resulting in -1. Thus, the correct answer is -1. The multiple-choice option for the answer is B. -1.
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