STATS Homework SP16

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 Y-axis.

B. Describe the scatterplot that you made in part A in terms of direction, shape, strength, and outliers.

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?

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?

F. How would you explain the results that you found in parts A through D to a statistics professor?

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 Y-axis.

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 andinterpretthe coefficient of determination for the relationship between wrist diameter and height.

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.

J. Harry’s actual weight is 70 kg. What is Harry’s residual?

K. Harry has no knowledge of statistics. How would you explain what his residual means to him?

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?

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.

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)