To compute the least-squares regression equation for the given data set, we need to find the slope ($m$) and the y-intercept ($b$) using the formula for the line of best fit, $\hat{y} = mx + b$.

The data provided are: $x: 5.8, 4.1, 6.5, 4.6, 6.6, 5.8, 5.2$ $y: 2.0, 4.9, 1.0, 4.1, 1.2, 1.9, 2.9$

Steps to calculate the least-squares regression equation:

1. Calculate the means of $x$ and $y$: $\bar{x} = \frac{\sum x}{n}, \quad \bar{y} = \frac{\sum y}{n}$

2. Calculate the slope $m$ using: $m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$

3. Calculate the y-intercept $b$ using: $b = \bar{y} - m\bar{x}$

Let me work on this and provide you with the regression equation.The least-squares regression equation for the given data set is:

$\hat{y} = -1.5599x + 11.1731$

This equation indicates that the slope is approximately $-1.5599$, and the y-intercept is approximately $11.1731$.

Would you like further details or have any questions? Here are five related questions you might consider:

1. What does the negative slope of $-1.5599$ indicate about the relationship between $x$ and $y$?
2. How can we calculate the correlation coefficient to measure the strength of this relationship?
3. Can we use this equation to make predictions for new values of $x$?
4. What is the importance of rounding the slope and intercept to four decimal places in regression analysis?
5. How would outliers in the data affect the regression equation?

Tip: When interpreting regression results, the slope tells you the change in the dependent variable $y$ for each unit increase in the independent variable $x$.