To compute the sum of the squared residuals, we need to calculate the residual for each point and then square it before adding the results.

The residual for a point $(x_i, y_i)$ is the difference between the actual $y_i$ value and the predicted $y_i$ value from the line equation $y = 1.75x + 1.5$.

Let's compute the residuals for both points:

1. For the point (-2, -2):

   • The actual $y$ value is -2.
   • The predicted $y$ value using $y = 1.75x + 1.5$ is: $y_{\text{predicted}} = 1.75(-2) + 1.5 = -3.5 + 1.5 = -2$
   • The residual is: $\text{residual} = y_{\text{actual}} - y_{\text{predicted}} = -2 - (-2) = 0$
   • Squared residual: $0^2 = 0$

2. For the point (2, 5):

   • The actual $y$ value is 5.
   • The predicted $y$ value using $y = 1.75x + 1.5$ is: $y_{\text{predicted}} = 1.75(2) + 1.5 = 3.5 + 1.5 = 5$
   • The residual is: $\text{residual} = y_{\text{actual}} - y_{\text{predicted}} = 5 - 5 = 0$
   • Squared residual: $0^2 = 0$

Sum of squared residuals:

$\text{Sum} = 0 + 0 = 0$

Thus, the sum of the squared residuals is 0.

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Would you like any additional details or clarifications?

Here are 5 related questions to expand on this topic:

1. What does a residual of 0 imply about the fit of the line to the points?
2. How would the sum of squared residuals change if the line did not pass through both points?
3. What is the general formula for calculating residuals for any given point?
4. How does least squares regression minimize the sum of squared residuals?
5. What is the significance of the slope and intercept in linear regression?

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