Final answer:
The machine would pick the predicted value for y when x equals d using the least-squares regression line, which minimizes the sum of squared residuals. This is an estimate based on the fitted line and may not match the actual value, which can be affected by factors like outliers.
Step-by-step explanation:
If a machine learns the least-squares regression line that best fits the data, the value it will pick for y when x is equal to d (a given value) will be the predicted value using the line. This is because a regression line represents the best estimate or prediction of y based on the given x-values. However, the actual value in the dataset may differ from this prediction; this difference is known as the residual or error.
The least-squares line minimizes the sum of the squares of the residuals across all points in the dataset, which is why it's often used for prediction. Calculating the least-squares line involves finding the slope (b) and the y-intercept (a) of the line that minimize these residuals. In the context of a scatter plot representing data, you can also examine the presence of any outliers and assess whether a linear model is appropriate.