The predict() function can be used to predict the probability that the market will go up, given values of the predictors. The type="response" option tells R to output probabilities of the form \(P(Y = 1|X)\), as opposed to other information such as the logit. If no data set is supplied to the predict() function, then the probabilities are computed for the training data that was used to fit the logistic regression model. Here we have printed only the first ten probabilities. We know that these values correspond to the probability of the market going up, rather than down, because the contrasts() function indicates that R has created a dummy variable with a 1 for Up.

> glm.probs <- predict(glm.fit, type = "response")
> glm.probs[1:10]
        1         2         3         4         5         6         7         8 
0.5070841 0.4814679 0.4811388 0.5152224 0.5107812 0.5069565 0.4926509 0.5092292 
        9        10 
0.5176135 0.4888378 
> contrasts(Direction)
     Up
Down  0
Up    1

Try calculating the probabilities for this model:

Assume that: