Final answer:
The line of best fit in a scatter plot is the line that represents the trend of the data by minimizing the distances of all points from the line, found using least-squares regression. It is obtained by visually or calculating a line that distributes data points evenly around it. The regression equation represents this line and can be used for predictive purposes.
Step-by-step explanation:
To determine the most accurate line of best fit for a scatter plot, one must analyze the way the data points are arranged. Ideally, the line of best fit should represent the trend of the data by minimizing the distances of all the points from the line (the residuals). In statistics, the method commonly used for this purpose is the least-squares regression.
Regression analysis helps us find the line that best predicts the dependent variable (in your case, height) based on the independent variable (shoe size). To construct a line of best fit, first plot the data points. Then, visually or through calculation, draw a line that appears to evenly distribute the points above and below it, with as many points as possible being close to the line. Pick two points on this line to determine the slope (change in height divided by the change in shoe size) and find the y-intercept (where the line crosses the y-axis), which gives you the starting point of the line when the independent variable is zero.
The equation of the line of best fit is expressed in the format y = mx + b, where m is the slope and b is the y-intercept. Not everyone will have the same equation because individual measurements and estimates differ. If the value of an r value is zero, it indicates no linear relationship between the variables. To find the predicted height for a pinky length of 2.5 inches, simply substitute 2.5 for the x value in your regression equation and solve for y.