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Answer :
Answer:
Step-by-step explanation:
The sum of the residuals for all the points is 19.
The residuals are the distances between the data points and the trend line. The black lines in the diagram represent the residuals. The sum of the residuals is calculated by adding up the lengths of all the black lines.
In this case, the sum of the residuals is 19. This means that the trend line is not a perfect fit for the data, but it is a good approximation.
To calculate the sum of the residuals, you can use the following formula:
```
sum of residuals = Σ(residual)^2
```
where Σ represents the sum of all the residuals, and residual is the distance between a data point and the trend line.
In this case, the residuals are:
* 4 for the point at (12, 96)
* 3 for the point at (16, 108)
* 2 for the point at (20, 120)
* 1 for the point at (24, 112)
* 0 for the point at (28, 104)
* -1 for the point at (32, 96)
* -2 for the point at (36, 88)
* -3 for the point at (40, 80)
The sum of the residuals is therefore:
```
sum of residuals = 4 + 3 + 2 + 1 + 0 + (-1) + (-2) + (-3) = 19
```
Therefore, the answer is 19.
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