Suppose we want to predict 2s and 7s in our mnist_27 dataset with just the second covariate. Can we do this? On first inspection it appears the data does not have much predictive power. In fact, if we...

Suppose we want to predict 2s and 7s in our mnist_27 dataset with just the second covariate. Can we do this? On first inspection it appears the data does not have much predictive power. In fact, if we fit a regular logistic regression, the coefficient for x_2 is not significant!

Fit a loess line to the data above and plot the results. Notice that there is predictive power, except the conditional probability is not linear.