Question 1180053
Here's how to graph the residuals and analyze the assumptions:

1. **Create a Scatterplot:**

* Plot the x-values on the horizontal axis and the residuals (y - ŷ) on the vertical axis.

2. **Analyze the Scatterplot:**

* **Linearity:** Look for a random scatter of points around the horizontal axis (y = 0). If there is a clear pattern (e.g., a curve), the linearity assumption might be violated.
* **Constant Variance (Homoscedasticity):** The spread of the residuals should be roughly constant across all x-values. If the spread increases or decreases as x increases, the constant variance assumption might be violated.
* **Normality:** While harder to assess visually, look for a roughly symmetric distribution of residuals around the horizontal axis. If the distribution is heavily skewed or has outliers, the normality assumption might be in jeopardy.
* **Independence:** This assumption is difficult to assess from a residual plot alone. However, if there is a clear pattern (e.g., a cyclical trend), it could suggest that the residuals are not independent.

**Analysis of Your Data:**

Based on the given data, here's what we can observe from a scatterplot of the residuals:

* **Linearity:** There seems to be a slight upward trend in the residuals as x increases. This could indicate a mild violation of the linearity assumption.
* **Constant Variance:** The spread of residuals appears to be relatively constant across the x-values, suggesting that the constant variance assumption is likely met.
* **Normality:** With only seven data points, it's difficult to assess normality visually. However, there are no extreme outliers or strong skewness.
* **Independence:** There is no clear pattern suggesting a violation of independence.

**Conclusion:**

Based on the residual plot, the linearity assumption might be slightly in jeopardy. However, with such a small sample size, it's difficult to draw definitive conclusions. Further analysis with more data points might be needed to confirm any violations.