Final answer:
Using the regression line to predict the y-value for x = 5.5 years involves calculating the prediction. The slope and y-intercept of the regression line provide information about the average change in y with respect to x and the predicted y-value when x is zero, respectively. Residuals indicate the accuracy of these predictions and can suggest the presence of outliers.
Step-by-step explanation:
If you are using the regression line to predict the y-value for x = 5.5 years, you would be calculating the prediction. The regression line is a tool used in statistics to estimate the relationship between two variables. When given a specific value of x, you can find its corresponding y-value on the regression line. This y-value is the predicted outcome based on the linear relationship modeled by the regression equation.
The slope of the regression line represents the average change in the dependent variable (y) for every one-unit change in the independent variable (x). The y-intercept is the predicted value of y when x equals zero. It's where the regression line crosses the y-axis on a graph.
To understand how well the regression line fits the data, we can look at indicators like the correlation coefficient or the coefficient of determination (r-squared value). A point with the largest residual is one where the actual y-value differs most from the predicted y-value given by the regression line. Residuals help in assessing the accuracy of the predictions. If the residual is too large, this point could be considered an outlier or an influential point.