Bivariate data for the quantitative 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. 7.5 8.8 11+ 2.9 1.8 10- 3.4 3.4 5.7 4.7 9+ 3.2 2.9 4.0 1.7 4.4 3.5 5.2 3.6 6.8 6.5 5+ 8.5 9.5 4.5 4.4 4+ 5.8 7.3 3+ 6.7 6.9 8.1 9.6 2+ 7.5 7.6 1+ 5.6 6.4 8.7 9.8 2. 9. 10 11 6.4 5.2
Bivariate data for the quantitative 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. 7.5 8.8 11+ 2.9 1.8 10- 3.4 3.4 5.7 4.7 9+ 3.2 2.9 4.0 1.7 4.4 3.5 5.2 3.6 6.8 6.5 5+ 8.5 9.5 4.5 4.4 4+ 5.8 7.3 3+ 6.7 6.9 8.1 9.6 2+ 7.5 7.6 1+ 5.6 6.4 8.7 9.8 2. 9. 10 11 6.4 5.2
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
Transcribed Image Text:**Bivariate Data Analysis**
The following table presents bivariate data for the quantitative variables \( x \) and \( y \). A scatter plot of this data is displayed next to the table, illustrating the relationship between the two variables.
**Data Table:**
| \( x \) | \( y \) |
|--------|--------|
| 7.5 | 8.8 |
| 2.9 | 1.8 |
| 3.4 | 3.4 |
| 5.7 | 4.7 |
| 3.2 | 2.9 |
| 4.0 | 1.7 |
| 4.4 | 3.5 |
| 5.2 | 3.6 |
| 6.8 | 6.5 |
| 8.5 | 9.5 |
| 4.5 | 4.4 |
| 5.8 | 7.3 |
| 6.7 | 6.9 |
| 10.6 | 8.8 |
| 7.5 | 7.6 |
| 8.1 | 9.6 |
| 5.6 | 4.4 |
| 8.7 | 9.8 |
| 6.4 | 5.2 |
**Scatter Plot Explanation:**
- The scatter plot is a graphical representation of the data with \( x \)-axis representing the variable \( x \) and the \( y \)-axis representing the variable \( y \).
- Each point on the plot corresponds to a pair of values \( (x, y) \) from the table.
- Observing the scatter plot, there appears to be a positive correlation between \( x \) and \( y \), meaning as \( x \) increases, \( y \) tends to increase as well.
- To better understand this relationship, one can sketch an approximation of the least-squares regression line, which minimizes the distance between the data points and the line itself.
You are encouraged to draw the least-squares regression line on the scatter plot to visually assess the strength and nature of the relationship between these variables.
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