0.6T 0.4+ 0.2- 0.0- -0.2+ -0.4+ -0.6+ -0.8+ -1.0- + + 3 + 4 + 1 8. 9. +5 2. Residuals

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Chapter1: Starting With Matlab
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Based on the plot, is it reasonable to conclude that a linear model is appropriate?

A. Yes, because the plot shows no apparent pattern.

B. Yes, because the points in the plot display less variation as \( x \) increases.

C. Yes, because the sum of the residuals is close to zero.

D. No, because the plot shows no apparent pattern.

E. No, because the points in the plot display more variation as \( x \) increases.
Transcribed Image Text:Based on the plot, is it reasonable to conclude that a linear model is appropriate? A. Yes, because the plot shows no apparent pattern. B. Yes, because the points in the plot display less variation as \( x \) increases. C. Yes, because the sum of the residuals is close to zero. D. No, because the plot shows no apparent pattern. E. No, because the points in the plot display more variation as \( x \) increases.
The following is a residual plot from a regression of a variable with the independent variable \( x \).

### Explanation of the Residual Plot

This plot displays the residuals on the y-axis versus the independent variable \( x \) on the x-axis. The residuals range from -1.0 to 0.6 and are plotted as black dots against values of \( x \) ranging from 0 to 8.

- **Horizontal Axis (x):** Represents the independent variable, \( x \), which takes on values from 0 to 8.
- **Vertical Axis (Residuals):** Displays the difference between the observed and predicted values from a regression analysis. The values range from -1.0 to 0.6.

The plot includes a horizontal reference line at the residual value of 0, helping to visualize deviations above and below zero.

**Interpretation:**
The residuals are scattered across the plot without forming a clear pattern, which is indicative of a good fit in regression. If a pattern were visible, it might suggest issues like non-linearity or heteroscedasticity that could affect the model's validity.
Transcribed Image Text:The following is a residual plot from a regression of a variable with the independent variable \( x \). ### Explanation of the Residual Plot This plot displays the residuals on the y-axis versus the independent variable \( x \) on the x-axis. The residuals range from -1.0 to 0.6 and are plotted as black dots against values of \( x \) ranging from 0 to 8. - **Horizontal Axis (x):** Represents the independent variable, \( x \), which takes on values from 0 to 8. - **Vertical Axis (Residuals):** Displays the difference between the observed and predicted values from a regression analysis. The values range from -1.0 to 0.6. The plot includes a horizontal reference line at the residual value of 0, helping to visualize deviations above and below zero. **Interpretation:** The residuals are scattered across the plot without forming a clear pattern, which is indicative of a good fit in regression. If a pattern were visible, it might suggest issues like non-linearity or heteroscedasticity that could affect the model's validity.
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