Stock Market Data consist of percentage return for the S&P 500 stock index over 1250 days (2001–2005). This data consists percentage return in 5 previous day and number of shares traded (in billions) on the previous day. Also there is information percentage return on every day over 2001–2005 and whether market was Up and Down based on the percentage return information. Then based on information of volume variable from data, number of shares traded over 2001–2005 tends to increase as show by the below graphic:

For this modeling to classify response of data, Stock Market Data divides to be 2 part that is data from 2001–2004 to be data training and for 2005 to be data test. Data training is used to estimate coefficient which use for qualitative prediction or classification model such as logistic regression. Also for qualitative prediction or classification response of data in this written are logistic regression, Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA) and K-Nearest Neighbors (KNN). Response of data is direction variable and this modeling in order to predict direction for a day is up or down based on the percentage return of the day. For other variable in the data is to be predictor variable. Those variables are percentage return in 5 previous days respectively and volume as number of shares traded.

## A. Logistic Regression

Classification of direction of a day is determined of probability which is obtained from the below equation: