Consider the table showing the given, predicted and residual values for a data set.

Which point would be on the residual plot of the data?

(1, –2.2)

(2, 1.5)

(3, 3.7)

(4, 0.1)

To determine which point would be on the residual plot, we need to understand what the residual plot represents. A residual plot shows the residuals on the y-axis and the corresponding x-values on the x-axis. The residual is the difference between the observed (given) value and the predicted value for each data point.

Here's how we would analyze the problem:

1. **Residual Calculation**: The residual for each data point is calculated as:
   \[
   \text{Residual} = \text{Given Value} - \text{Predicted Value}
   \]

2. **Identifying the Residual Point**: The residual plot has x-values on the x-axis and corresponding residuals on the y-axis. If you have the given values, predicted values, and residuals, you can plot the residuals against the x-values.

To determine which point would be on the residual plot, it must match the residuals calculated from the dataTo determine which point would be on the residual plot, we need to understand what the residual plot represents. A residual plot shows the residuals on the y-axis and the corresponding x-values on the x-axis. The residual is the difference between the observed (given) value and the predicted value for each data point.

Here's how we would analyze the problem:

1. **Residual Calculation**: The residual for each data point is calculated as:
   \[
   \text{Residual} = \text{Given Value} - \text{Predicted Value}
   \]

2. **Identifying the Residual Point**: The residual plot has x-values on the x-axis and corresponding residuals on the y-axis. If you have the given values, predicted values, and residuals, you can plot the residuals against the x-values.

To determine which point would be on the residual plot, it must match the residuals calculated from the 

- **Point (1, -2.2)** suggests that when \( x = 1 \), the residual is \(-2.2\).
- **Point (2, 1.5)** suggests that when \( x = 2 \), the residual is \(1.5\).
- **Point (3, 3.7)** suggests that when \( x = 3 \), the residual is \(3.7\).
- **Point (4, 0.1)** suggests that when \( x = 4 \), the residual is \(0.1\).

To match one of these points to the actual residual plot, you'd need to calculate the residuals from the given and predicted values for each corresponding \( x \) value. The point where the residual value matches exactly with one of these pairs will be on the residual plot.

Without specific data, it's not possible to definitively state which point corresponds to the residual, but each point listed is a candidate depending on the specific calculations made.

If you have the residuals, simply match them to find which pair fits, and that will be the point on the residual plot.

Would you like details on how to calculate residuals or any other questions?

**Relative questions:**

1. How do you calculate residuals using given and predicted values?
2. What does it mean if the residual plot shows a clear pattern?
3. How can you interpret a residual plot that shows random distribution?
4. Why is it important to analyze residuals in regression analysis?
5. Can a residual plot help identify outliers in the data set?

**Tip:** A good residual plot should show no apparent pattern, indicating that the model fits the data well.

Explore how residual plots are used in data analysis to visualize the differences between given and predicted values. Learn about calculating residuals and interpreting their significance. Suitable for high school students studying data analysis.

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