Lesson 12: Regression NAME Lab Assignment 1. Using the Class Survey data set, create a correlation matrix in Mintab for the following variables: GPA, Drinking Days, and Miss Class (number of classes missed) (instead of obtaining the correlation for two variables, enter in all three and you will get a matrix that indicates the correlation between all pairs of variables). Based on this correlation matrix, what variable would best be used in a regression model with one predictor variable that is seeking to predict GPA? Why? Also, Copy and Paste your correlation matrix. 2. Use the file BodyData.MTW to answer the following questions. ( 20 points) A. Create a scatterplot with height on the X-axis and wrist diameter on the Y-axis. Copy and Paste your scatterplot. Describe the scatterplot in terms of direction, shape, strength, and outliers. (2 pts of 20) 1 Lesson 12: Regression NAME Lab Assignment Summary Statistics Variable Wrist Diameter Height (cm) N Mean StDev Minimum Maximum 145 11.1993 0.65442 9.80000 13.3000 145 177.519 7.5196 157.200 198.100 Regression Equation Wrist Diameter = 5.237 + 0.033586 Height (cm) B. Use the five-step hypothesis testing procedure to determine if there is a statistically significant relationship between height and wrist diameter. (Use Pearson's r) (5 pts of 20) 1) Check necessary assumptions and write null hypothesis Ho: p=0 Ha: p0 2) Calculate appropriate test statistic 3)Determine p value 4) Decide between null and alternative 5) State real world conclusion C. Use the five-step hypothesis testing procedure to determine if height is a statistically significant predictor of wrist diameter. In other words, test for the significance of the slope in the simple linear regression model. Assume that all assumptions are met. (5 pts of 20) D. Now reverse the response and predictor variables. Use the five-step hypothesis testing procedure to determine if wrist diameter is a statistically significant predictor of height. Check all assumptions and (5 pts of 20) 2 Lesson 12: Regression NAME Lab Assignment E. How was the regression model impacted when the X and Y variables were switched? (i.e., compare the regression models from parts C and D) F. Compare the p values from parts B, C, and D. G. Compute and interpret the coefficient of determination for the relationship between wrist diameter and height from part D. 3 Lesson 12: Regression NAME Lab Assignment 3. A professor is concerned that a couple of his students may be cheating on their homework assignments. He would like to use regression methods to try to determine which students he should be concerned about cheating. He creates a simple linear regression model using homework grades to predict exam grades. His output follows. (5 points) 4 Lesson 12: Regression NAME Lab Assignment Regression Equation Exam = 12.905 + 0.7843 Homework 5 Lesson 12: Regression NAME Lab Assignment Discuss how this professor could use this information to identify students who may be cheating. 6