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This paper describes a machine learning method, called Regression by Selecting Best Feature Projections (RSBFP). In the training phase, RSBFP projects the training data on each feature dimension and aims to find the predictive power of each feature attribute by constructing simple linear regression lines, one per each continuous feature and number of categories per each categorical feature. Because, although the predictive power of a continuous feature is constant, it varies for each distinct value of categorical features. Then the simple linear regression lines are sorted according to their predictive power. In the querying phase of learning, the best linear regression line and thus the best feature projection are selected to make predictions.