To find the regression of the given data sets $X$ and $Y$, we will use the method of least squares to find the equation of the best-fit line, typically expressed as:

$Y = a + bX$

where:

• $b$ is the slope of the line.
• $a$ is the y-intercept.

The formulas for $a$ and $b$ are:

$b = \frac{n\sum{XY} - \sum{X}\sum{Y}}{n\sum{X^2} - (\sum{X})^2}$

$a = \frac{\sum{Y} - b\sum{X}}{n}$

where:

• $n$ is the number of data points.
• $\sum{X}$ is the sum of all $X$ values.
• $\sum{Y}$ is the sum of all $Y$ values.
• $\sum{XY}$ is the sum of the product of corresponding $X$ and $Y$ values.
• $\sum{X^2}$ is the sum of the squares of $X$ values.

Let's calculate the values.The regression equation for the given data is:

$Y = 4.75 + 5.32X$

This means the best-fit line that describes the relationship between $X$ and $Y$ can be expressed as $Y = 4.75 + 5.32X$.

Would you like more details or have any questions about this process?

Here are five related questions you might consider:

1. How do you interpret the slope $b$ in the context of this data?
2. What does the y-intercept $a$ represent in this regression equation?
3. How would you calculate the correlation coefficient for this data set?
4. How can you determine if the regression model is a good fit for the data?
5. What are the assumptions underlying linear regression?

Tip: In regression analysis, the slope represents the change in the dependent variable (Y) for every one-unit increase in the independent variable (X).