What happens to the accuracy of y predictions if the residual values increase as x values increase?

When the residual values, which represent the differences between the actual values and the predicted values, increase as the x values increase, it indicates that the model is not fitting the data well, particularly at higher levels of x. This means that the model’s predictions become less accurate because the errors in those predictions are growing larger.

In statistical terms, increasing residuals suggest that the assumptions of the regression model may not hold true for the range of the x values being considered. A good model should show constant residuals across all levels of x (homoscedasticity). When residuals increase, it could signify that there is a non-linear relationship that has not been captured by the model or that there are outliers affecting the prediction accuracy.

Thus, when residual values increase with increasing x values, it is reasonable to conclude that the accuracy of predictions for y deteriorates, leading to the conclusion that the accuracy decreases.