Lesson 12: Regression Lab Assignment Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. Use an alpha level of .05 unless otherwise specified. 1. Use the file SP16STUDENTDATA.MTW to answer the following questions. (40 points) A. Create a scatterplot with height on the X-axis and shoe size on the Yaxis. B. Describe the scatterplot that you made in part A in terms of direction, shape, strength, and outliers. The direction is positive, the outliers are all of the scattered dots outside of clustered area, and it is strong because it is positive and placed over to the right Lesson 12: Regression Lab Assignment C. Would it be appropriate to compute a Pearson's r as a measure of the relationship between these two variables? Why or why not? Yes, Because the stronger the association between the two variables, the closer the Pearson correlation coefficient will be to -1 or in this case +1. All of the data points are included on the line of best fit D. Compute the correlation (Pearson's r) for the relationship between height and shoe size and use the five-step hypothesis testing procedure to determine if the correlation is statistically significant. E. How would you explain the results that you found in parts A through D to a friend with no knowledge of statistics? The scatterplot is going up and to the right, this is a positive correlation. Outliers are values outside of the normal range of values or the dots not grouped with others. F. How would you explain the results that you found in parts A through D to a statistics professor? This is a strong positive correlation because it is going up and to the right. Also, there is a relationship between the two variables. High scores on height is just as likely to occur with high scores on shoe size 2. Use the file BodyData.MTW to answer the following questions. (45 points) A. Create a scatterplot with height on the X-axis and wrist diameter on the Yaxis. Lesson 12: Regression Lab Assignment 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) 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. Don't forget to check all of the necessary assumptions! D. Use the five-step hypothesis testing procedure to determine if wrist diameter is a statistically significant predictor of height. All assumptions have been met. 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. The dependent variable height is getting explained by the independent variable wrist diameter. H. Use the five-step hypothesis testing procedure to determine if height is a statistically significant predictor of weight. All assumptions have been met. I. Harry is an adult. He is 165 cm tall. Use your regression equation from part H to predict Harry's weight. Lesson 12: Regression Lab Assignment Height = J. Harry's actual weight is 70 kg. What is Harry's residual? Residual = Actual-Predicted = 70 K. Harry has no knowledge of statistics. How would you explain what his residual means to him? It means that he is taller than a person with an average height with his traits L. Levi is 7 years old. Would it be appropriate to use your regression model from part H to compute his residual? Why or why not? Levi is still not an adult and the regression model is based on the data of an adult so the regression model would not work here. Lesson 12: Regression 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. Lesson 12: Regression Regression Equation Exam = 12.905 + 0.7843 Homework Lab Assignment Lesson 12: Regression Lab Assignment Discuss how this professor could use this information to identify students who may be cheating. It is expected that it will take around 75-100 words to fully answer this question. (15 points)