The chart represents a data set's given values, predicted values (using a line of best fit for the data), and residual values.
| x | Given | Predicted | Residual |
|---|---|---|---|
| 1 | 6 | 7 | -1 |
| 2 | 12 | 11 | 1 |
| 3 | 13 | 15 | g |
| 4 | 20 | 19 | h |
Which are the missing residual values?
A. g=2 and h=-1
B. g=28 and h=39
C. g=-2 and h=1
D. g=-28 and h=-39
Answer (1)
Calculate g by subtracting the predicted value from the given value when x=3: g = 13 − 15 = − 2 .
Calculate h by subtracting the predicted value from the given value when x=4: h = 20 − 19 = 1 .
The missing residual values are g = − 2 and h = 1 .
The final answer is g = − 2 and h = 1 .
Explanation
Understanding the Problem We are given a table with data, predicted values, and residual values. The residual is the difference between the given value and the predicted value. We need to find the missing residual values, g and h .
Calculating g To find g , we subtract the predicted value at x = 3 from the given value at x = 3 . So, g = 13 − 15 = − 2 .
Calculating h To find h , we subtract the predicted value at x = 4 from the given value at x = 4 . So, h = 20 − 19 = 1 .
Final Answer Therefore, the missing residual values are g = − 2 and h = 1 .
Examples
Understanding residuals is crucial in analyzing the accuracy of predictions. For instance, in weather forecasting, the residual is the difference between the actual temperature and the predicted temperature. Similarly, in stock market analysis, residuals help assess the reliability of investment predictions. By analyzing residuals, we can refine our models and make more accurate predictions in various real-world scenarios.
