Final answer:
The correct answer is that each point in the data set is near the regression line. The slope and y-intercept of the regression model provide valuable insights into the relationship between the two variables. Residuals are used to determine how well the regression line fits the data, with the largest residual potentially indicating an outlier or an influential point.
Step-by-step explanation:
The most likely true statement about the data set represented by the regression model on the graph is that each point in the data set is near the regression line. It is important to recognize that real data may have some inaccuracies, and as a result, the plotted points may not all fall exactly on the trend line, which is intended to represent the general pattern of the data. When considering the regression line, we also take into account concepts like the slope and the y-intercept, which provide us with important information about the relationship between the variables.
The slope of the regression line indicates the rate of change between the independent variable (x) and the dependent variable (y). In other words, it tells us how much the dependent variable is expected to change for each one-unit increase in the independent variable. The y-intercept represents the value of y when x is 0 and gives us a starting point for the regression line on the y-axis. When it comes to how well the regression line fits the data, we can look at the residuals, which are the differences between the actual values and the estimated values of y. The point with the largest residual is the one that lies farthest from the regression line, which could possibly be an outlier or an influential point. Whether a linear relationship exists between the variables can be tested with statistical methods, such as calculating the significance of the correlation coefficient at a certain significance level.