Cumulative Assessment
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(54,-72) (60,-10) (68,26) (72,94) (78,96) (84,58) (92,-6) and (98,-64)
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A residual is the difference of the y-value of the data point and the corresponding y-value found using the line of fit. |
We know that the data can be modeled by the equation y=3x-50. Let's calculate the residuals for the given data set.
| x | Observed y | y from model | Residual |
|---|---|---|---|
| 54 | 40 | 3* 54-50= 112 | 40- 112= -72 |
| 60 | 120 | 3* 60-50= 130 | 120- 130= -10 |
| 68 | 180 | 3* 68-50= 154 | 180- 154= 26 |
| 72 | 260 | 3* 72-50= 166 | 260- 166= 94 |
| 78 | 280 | 3* 78-50= 184 | 280- 184= 96 |
| 84 | 260 | 3* 84-50= 202 | 260- 202= 58 |
| 92 | 220 | 3* 92-50= 226 | 220- 226= -6 |
| 98 | 180 | 3* 98-50= 244 | 180- 244= -64 |
Based on the above calculations, eight of the given points will appear on the scatter plot of residuals. (54,-72), (60,-10), (68,26), (72,94), (78,96), (84,58), (92,-6), and (98,-64)
By studying these residuals we can see that the model is not a good fit for the data. While the residuals are centered about the x-axis, they are not random.
The residuals form a ⋂-shaped pattern. This tells us that the data is not linear, and consequently the given linear equation is not a good fit for the data.