IE 7280 Lab3-4

1 Lab # 3 & Lab#4 Conducted Week (10/20 , 10/27 ) Regression and Prediction For this Lab, work in groups with 2 students. Each group will turn in a single group assignment. This Lab involves predicting a person's weight (the response variable y), based on a number of factors (x 1 through x 8 below). y: weight (pounds) x 1 : height (inches) x 2 : gender (male = 1; female = 0) x 3 : average number of meat servings (4 oz.) consumed each day x 4 : average number of fruit or vegetable servings consumed each day x 5 : age (years) x 6 : carries cell phone regularly (yes = 1; no = 0) x 7 : last digit of home phone number x 8 : will Cubs win the World Series? (Yes = 1; No = 0) This lab involves two separate sets of data: The training set (in Lab 3 Training.csv) are the preceding variables collected for 22 students in the Fall, 2006 IEMS 304 class (each row = one person; each column = one variable). The test set (in Lab 3 Test.csv) are the same variables collected for 136 students in other years. You will fit a regression model to the training data. Then, you will use the model fitted to the training data to see how well you can predict the responses for the data in the test data. Do NOT include the test data when fitting the regression model. 1) For the training data, construct and interpret a scatter-plot matrix of all variables (response and predictors). Are any relationships between y and the predictor variables apparent? 2) Using the training data, fit a regression model that includes all eight predictor variables . Use this fitted model to predict the weights for everyone in the test set. Construct a scatter plot of y versus y ˆ (y on the vertical axis) for all observations in the training set and in the test set together (i.e., a single plot), but distinguish the training group and the test group using two different symbols. Discuss the significance of what you see. 3) Calculate 95% prediction intervals for the weights of everyone in the test set, and also calculate the prediction errors. The "prediction errors" are defined as the residual errors ( y − y ˆ ) for predicting the test data, using the coefficients estimated from the training data. Hence, you have one prediction error for each person in the test set. Lab 3 (week, 10/2 0 )