Final answer:
A regression line for a set of points is calculated using the least-squares method to show the dependence of y on x. Outliers may be removed for a more accurate line, and the equation of the line allows for predictions of unknown y values for given x values.
Step-by-step explanation:
You are asking about finding a regression line for a given set of points. This is a process used in statistics to determine a line that best fits the data on a scatter plot, showing the dependence of y on x. The equation of a regression line is typically written as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the regression line for the given points, you would use the least-squares method, which minimizes the sum of the squares of the vertical distances of the points from the line. Once the line is calculated, it can be used to predict the value of y for any given value of x. For example, if you have a regression line equation of y = 5 + 0.3x, you can predict y for x = 2 as 6.2, which would not be considered an outlier if the standard deviation of the residuals is 0.4.
The process of drawing a regression line can also include removing outliers which are points that do not fit well with the rest of the data. After removing an outlier and recalculating the regression line, the new equation and correlation coefficient might change, as seen in the provided example where the new line of best fit is ŷ = -355.19 + 7.39x and the correlation coefficient is r = .9121.