Bivariate data for the guantitative variables x and y are given in the table below. These data are plotted in the scatter plot shown next to the table. In the scatter plot, sketch an approximation of the least-squares regression line for the data. y 5.8 6.7 11+ 7.4 8.3 10+ 3.1 1.8 4.6 4.0 9+ 3.0 0.8 8- 5.9 6.6 4.9 3.7 7+ 6.7 7.3 6- 6.7 4.8 5+ 3.4 2.7 7.8 8.1 4+ 7.0 5.9 3+ 3.6 1.8 3.9 3.7 5.7 4.8 8.3 9.7 9.0 9.8 10 11 8.0 8.3

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### Understanding Bivariate Data and Regression Analysis

**Bivariate Data Table:**

The table presents quantitative variables \( x \) and \( y \):

| \( x \) | \( y \) |
|---------|---------|
| 5.8     | 6.7     |
| 7.4     | 8.3     |
| 3.1     | 1.8     |
| 4.6     | 4.0     |
| 3.0     | 0.8     |
| 5.9     | 6.6     |
| 4.9     | 3.7     |
| 6.7     | 7.3     |
| 6.7     | 4.8     |
| 3.4     | 2.7     |
| 7.8     | 8.1     |
| 7.0     | 5.9     |
| 3.6     | 1.8     |
| 3.9     | 3.7     |
| 5.7     | 4.8     |
| 8.3     | 9.7     |
| 9.0     | 9.8     |
| 8.0     | 8.3     |

**Scatter Plot:**

- The scatter plot visualizes the relationship between the \( x \) and \( y \) values.
- Each point represents a data pair from the table.
- The \( x \)-axis ranges from 1 to 11, while the \( y \)-axis ranges from 0 to 11.
- A general upward trend is observed in the data points, indicating a positive correlation between \( x \) and \( y \).

**Least-Squares Regression Line:**

- The graph prompts sketching an approximate least-squares regression line.
- This line minimizes the sum of the squared differences between observed values and the values predicted by the line.
- The icon next to the graph suggests tools for drawing or interacting with the plot.

For a more detailed study, analyze the scatter plot to assess the strength and direction of the linear relationship, which aids in understanding how variable \( y \) changes with \( x \).
Transcribed Image Text:### Understanding Bivariate Data and Regression Analysis **Bivariate Data Table:** The table presents quantitative variables \( x \) and \( y \): | \( x \) | \( y \) | |---------|---------| | 5.8 | 6.7 | | 7.4 | 8.3 | | 3.1 | 1.8 | | 4.6 | 4.0 | | 3.0 | 0.8 | | 5.9 | 6.6 | | 4.9 | 3.7 | | 6.7 | 7.3 | | 6.7 | 4.8 | | 3.4 | 2.7 | | 7.8 | 8.1 | | 7.0 | 5.9 | | 3.6 | 1.8 | | 3.9 | 3.7 | | 5.7 | 4.8 | | 8.3 | 9.7 | | 9.0 | 9.8 | | 8.0 | 8.3 | **Scatter Plot:** - The scatter plot visualizes the relationship between the \( x \) and \( y \) values. - Each point represents a data pair from the table. - The \( x \)-axis ranges from 1 to 11, while the \( y \)-axis ranges from 0 to 11. - A general upward trend is observed in the data points, indicating a positive correlation between \( x \) and \( y \). **Least-Squares Regression Line:** - The graph prompts sketching an approximate least-squares regression line. - This line minimizes the sum of the squared differences between observed values and the values predicted by the line. - The icon next to the graph suggests tools for drawing or interacting with the plot. For a more detailed study, analyze the scatter plot to assess the strength and direction of the linear relationship, which aids in understanding how variable \( y \) changes with \( x \).
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