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 [tex]x=4[/tex], 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'. The residual is calculated as the difference between the 'Given' value and the 'Predicted' value. Our goal is to find the residual when x = 4 .
Calculating the Residual 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: R es i d u a l = G i v e n − P re d i c t e d R es i d u a l = 9 − 10
Final Answer Performing the subtraction, we get: R es i d u a l = − 1 Therefore, the residual when x = 4 is -1.
Examples
In data analysis, residuals help assess the accuracy of a predictive model. For example, if you're predicting sales based on advertising spend, the residual is the difference between the actual sales and the sales your model predicted. A small residual indicates a good fit, while a large residual might suggest your model needs improvement or that other factors are influencing sales. By analyzing residuals, businesses can refine their forecasting models and make better decisions.
The residual when x = 4 is calculated by subtracting the predicted value from the given value, which gives − 1 . This corresponds to option B. Therefore, the answer is − 1 .
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