To determine the line of best fit, we need to apply the least squares method, which calculates the slope and y-intercept of the line that best fits the given data points. We are looking for an equation in the form:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Let's go through the necessary steps to find the equation of the line of best fit.

1. Mean of x and y:

We begin by calculating the mean of the $x$ values and the mean of the $y$ values.

2. Calculate slope (m):

The slope $m$ is given by the formula:

$m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$

3. Calculate intercept (b):

The intercept $b$ is given by the formula:

$b = \bar{y} - m\bar{x}$

I'll calculate the slope and intercept to get the line of best fit.The equation of the line of best fit is:

$y = 0.79x + 2.90$

This corresponds most closely to the option:

$y = 0.8x + 2.7$

Would you like further details on the calculations or steps? Here are five related questions:

1. How is the least squares method used to find the best fit line?
2. What is the significance of the slope and y-intercept in this context?
3. How can you calculate the correlation coefficient for this data set?
4. What are some limitations of using linear regression for non-linear data?
5. How do you determine if a linear model is appropriate for the given data?

Tip: When calculating the line of best fit, rounding is important to match the answer choices.