find the residual values, and use the graphing calculator tool to make a residual plot.\ndoes the residual…

find the residual values, and use the graphing calculator tool to make a residual plot.\ndoes the residual plot show that the line of best fit is appropriate for the data?\n|x|given|predicted|residual|\n|----|----|----|----|\n|1|3.5|4.06|\n|2|2.3|2.09|\n|3|1.1|0.12|\n|4|-2.2|-1.85|\n|5|-4.1|-3.82|\nyes, because the points have no clear pattern.\nno, the points have no pattern.\nno, the points are in a linear pattern.\nyes, the points are in a curved pattern.
Answer
Answer:
| x | Given | Predicted | Residual |
|---|---|---|---|
| 1 | 3.5 | 4.06 | $3.5 - 4.06=- 0.56$ |
| 2 | 2.3 | 2.09 | $2.3 - 2.09 = 0.21$ |
| 3 | 1.1 | 0.12 | $1.1 - 0.12=0.98$ |
| 4 | -2.2 | -1.85 | $-2.2-(-1.85)=-2.2 + 1.85=-0.35$ |
| 5 | -4.1 | -3.82 | $-4.1-(-3.82)=-4.1 + 3.82=-0.28$ |
| Answer for the second - part: Yes, because the points have no clear pattern. |
Explanation:
Step1: Recall residual formula
Residual = Given - Predicted
Step2: Calculate residual for x = 1
$3.5-4.06=-0.56$
Step3: Calculate residual for x = 2
$2.3 - 2.09=0.21$
Step4: Calculate residual for x = 3
$1.1-0.12 = 0.98$
Step5: Calculate residual for x = 4
$-2.2-(-1.85)=-0.35$
Step6: Calculate residual for x = 5
$-4.1-(-3.82)=-0.28$
Step7: Analyze residual plot
A good residual plot for a linear regression has no clear pattern (randomly - scattered points). So, the line of best fit is appropriate when there is no clear pattern in the residual plot.