Removing the point (5, 160) would likely result in changes to the slope, y-intercept, prediction accuracy, and residuals of the least-squares regression line.
Removing the point (5, 160) from the dataset and recalculating the least-squares regression line would have the following effects:
1. Change in slope: The slope of the regression line represents the relationship between the independent variable (x) and the dependent variable (y). Removing a data point can alter the overall trend and relationship between the variables, potentially changing the slope of the regression line. The new line may have a steeper or shallower slope depending on the impact of the removed point on the overall pattern.
2. Change in y-intercept: The y-intercept of the regression line represents the predicted value of the dependent variable when the independent variable is zero. Removing a point can affect the y-intercept, potentially shifting the line up or down.
3. Change in prediction accuracy: The least-squares regression line is designed to minimize the sum of the squared differences between the observed data points and the predicted values on the line. Removing a data point may change the accuracy of the line in predicting the remaining data. The removed point may have had a significant influence on the overall fit of the line, and its removal can affect the overall goodness of fit.
4. Change in residuals: Residuals represent the vertical distances between the observed data points and the predicted values on the regression line. Removing a point can change the residuals, potentially reducing or increasing the discrepancies between the observed and predicted values.