Maths - Minitab Assignment on Regression

Math 2208 Minitab Assignment on Regression (Ch. 7-9) Summer 2014

Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting and exercise. In this assignment you will look at the relationship between lean body mass (in kilograms, which is a person’s weight, leaving out all fat) and metabolic rate, which is measured in calories burned per 24 hours. We will use regression analysis to examine this relationship. If necessary, refer to the Minitab Survival Guide in the Lab Manual for more help.

1.Open the Minitab file bodymass.MTW from your class Moodle site by clicking on the file-it will open in Minitab automatically. In this file the column Mass is the lean body mass and Rate is the metabolic rate.

2. Type your name and ID in the session window, and Display the variables in your Session window with Data> Display Data....

3. Make a scatterplot of Rate vs. Mass, with the regression line plotted on it. To do this, click on

Stat > Regression > Fitted Line Plot....

Rate is the response variable, Y, and Mass the explanatory or predictor variable, X. Click OK. Print out a copy of this graph. The regression output will appear in your session window.

4. Perform the regression of rate on mass, and find the predicted metabolic rate for a person with lean body mass of 51 kilograms. You will also get residual plots:

Stat – Regression-Regression …,

choose Rate as the response, Mass as the Predictor,

choose Options, and fill in 51 in the Prediction intervals for new observations box,

then hit OK.

Choose Graphs .. and select Four in one then hit OK and OK

The result will appear in the Session window, the plots in a separate window. Print the plots.

5. Determine the correlation coefficient using Stat > Basic Statistics > Correlation..., again specifying the appropriate Y and X variables. Uncheck the box “Display p-values” before clicking OK.

6 Print out a copy of the Session window, and exit Minitab.

Answer the questions in the spaces provided on the following page. Note: When asked to highlight something on the output, it is fine to circle it with pen or pencil.

When passing in your assignment make sure to include: your answers, the plots and the session window. Make sure to staple the pages!

MATH2208 Assignment on regression Name____________________________

(i) Write a description of the relationship seen on the scatterplot, in context.

(Note the shape of the scatterplot: if the relationship is not at least roughly linear or if there are outliers, then linear regression may not be appropriate, although Minitab would still gladly do the calculations).

(ii) Highlight the slope on the output and interpret the value in the context of the problem.

(iii) Interpret the value of R2 (also called r2, or R-sq on Minitab output) in the context of the problem.

(iv) State the correlation, and the value of Rsq; highlight them on the output. Illustrate the relationship between the correlation and R2, i.e. how one is calculated from the other.

Correlation:___________________ Rsq ____________________

Relationship:

(v) State the regression equation, and highlight it on your output. ___________________________

By hand, find the predicted y-value for the lean body mass of 51 kilograms, showing your work below

Predicted value =_________

Find the predicted value for the lean body mass of 51 kilograms on the output and highlight it.

How does the value on the output compare with your calculation above? _____________________________

(vi) Discuss if the following conditions are satisfied, referring to your plots in your answers:

Straight Enough Condition:

Does the Plot Thicken? Condition: