Final answer:
The equation of the regression line, which represents a best-fit line through a data set on a scatter plot, is given by 'îy = -173.51 + 4.83x', where the slope is '4.83' and the y-intercept is '-173.51'.
Step-by-step explanation:
The equation of the regression line is a mathematical representation of the best-fit line through a set of data points on a scatter plot. The equation given in this example, 'ŷ = -173.51 + 4.83x', follows the standard form y = mx + b, where m represents the slope of the line and b represents the y-intercept. The negative value of the intercept, '-173.51', indicates the point where the regression line would cross the y-axis if extended, while '4.83' is the slope indicating how much ŷ (the predicted value of y) increases with each one-unit increase in x (the independent variable).
In any analysis, it is essential to ensure that the regression line is suitable for prediction purposes by examining the scatter plot and testing the significance of the correlation coefficient. Additionally, the coefficient of determination, denoted as r², shows the proportion of the variance in the dependent variable that is predictable from the independent variable.