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# Multiple Regression Analysis in Minitab

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BC LUMBER is trying to obtain a better prediction on the volume of its trees. A
sample of trees of various diameters were cut and the diameters, heights and volumes were recorded. The results are given below.

DIAMETER: Diameter in inches at 4.5 feet above ground level

HEIGHT: Height of the tree in feet

VOLUME: Volume of tree in cubic feet

DIAMETER HEIGHT VOLUME

8.3 70 10.3
8.6 65 10.3
8.8 63 10.2
10.5 72 16.4
10.7 81 18.8
10.8 83 19.7
11.0 66 15.6
11.0 75 18.2
11.1 80 22.6
11.2 75 19.9
11.3 79 24.2
11.4 76 21.0
11.4 76 21.4
11.7 69 21.3
12.0 75 19.1
12.9 74 22.2
12.9 85 33.8
13.3 86 27.4
13.7 71 25.7
13.8 64 24.9
14.0 78 34.5
14.2 80 31.7
14.5 74 36.3
16.0 72 38.3
16.3 77 42.6
17.3 81 55.4
17.5 82 55.7
17.9 80 58.3
18.0 80 51.5
18.0 80 51.0
20.6 87 77.0

Using MINITAB perform the regression and correlation analysis for the data on
VOLUME and DIAMETER and HEIGHT by answering the following:

1. Determine the regression equation which describes the relationship between
VOLUME, DIAMETER and HEIGHT.

2. Test the utility of this regression model using the F-test. Interpret the observed
p-value for this test.

3. Test the utility of each component of the model (i.e, is DIAMETER useful in
predicting VOLUME, and is HEIGHT useful in predicting VOLUME). Perform the
t-tests on Ã?²1 and Ã?²2 , report the t-values and observed p values and
interpret.

4. Determine the correlation matrix for VOLUME, HEIGHT and DIAMETER.

5. Find and interpret the multiple index of determination (R-Squared).

6. Find and interpret the 95% prediction interval for volume of a tree having
diameter of 15 inches and height 80 feet.

7. Find and interpret the 95% confidence interval for the mean volume for trees
having diameter of 15 inches and height 80 feet.

8. What volume would you predict for a tree having diameter 15 inches and height
120 feet?

9. What volume would you predict for a tree having diameter 30 inches and height
120 feet?

10. Based on your findings in 1-11 and your work in CASE #9, what is your opinion about using diameter and height to predict volume of trees? Explain.

11. Based on your analysis can you conclude that the diameter and the height cause the volume? Explain.

https://brainmass.com/statistics/regression-analysis/multiple-regression-analysis-in-minitab-431962

#### Solution Summary

The solution provides step by step method for the calculation of regression analysis in Minitab and Excel. Formula for the calculation and Interpretations of the results are also included.

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## Century National Bank - Minitab

I need help running multiple regression analysis in Minitab. Please do not use Excel.

See attached files. One is in WORD, the other is MINITAB.

Question 1 - Background to Century National Bank

The bank would like to know the characteristics of checking account customers. What is the balance of a typical customer? How many other bank services do the checking account customers use? Do the customers use the ATM service and, if so, how often are they used?

You are the head of the team and responsible for preparing the report. You select a random sample of 60 customers. In addition to the balance in each account at the end of last month, you determine: (1) the number of ATM (automatic teller machine) transactions in the last month; (2) the number of other bank services (a savings account, a certificate of deposit, etc.) the customer uses; (3) whether the customer has a debit card (this is a relatively new bank service in which charges are made directly to the customer's account); and (4) whether or not interest is paid on the checking account. The sample includes customers from the branches in Cincinnati, Ohio; Atlanta, Georgia; Louisville, Kentucky; and Erie, Pennsylvania.

These data are contained in the data file CNB60.MTB and have the following variable definitions:

Variable Description
Balance Account balance in \$
ATM Number of ATM transactions for the month
Services Number of other bank services used
Debit Has a debit card (0 = no, 1 = yes)
Interest Receives interest on the account (0 = no, 1 = yes)
City City where banking is done (1=Cincinnati, 2=Atlanta, 3=Louisville, 4=Erie, PA)

Refer to the description of Century Nation Bank in the Background section above. Using checking account balance as the response (Y) variable and using either the individual has a debit card variable OR whether interest is paid on the particular account as your predictor variable, write a report indicating how account balance relates to your predictor variable. Those seeking more adventure can do a 2-sample t-test since the debit card and interest variables are binary [each takes on two values]. How to the regression results compare to the 2-sample t-results. Check the p-values on your results using a significance level of &#945; = 0.05.

Don't forget question 2 that follows.
Question 2. Fun with regression. Brand New Question

For the following regression data sets (4 of them), do the following activities in order. It is very important that you do each step in sequence. You can easily highlight the data table below and copy and paste to MINITAB.

a. Run the simple linear regressions and report the four estimated regression equations. The response variables are YA, YB, YC, and YD. The predictor variables are XA, XB, XC, and XD. Keep the pairs together (YA with XA and so on). You should be able to summarize the four regression equations that you obtained in a few sentences.

b. Do a scatterplot of each of the data sets. Do the scatter plots match your expectations based on part a above? Just be honest. A few sentences should be sufficient.

c. Do a plot of residuals for each of the data sets. Make comparisons between the scatterplot and residual plot for each model. Again a few sentences should suffice for each model.

The data set contains four pairs of X and Y values. Model 1 has variables XA and YA, Model 2 has variables XB and YB, and so on.

YA XA YB XB YC XC YD XD
8.04 10 9.14 10 7.46 10 6.58 8
9.96 14 8.1 14 8.84 14 5.76 8
5.68 5 4.74 5 5.73 5 7.71 8
6.95 8 8.14 8 6.77 8 8.84 8
8.81 9 8.77 9 7.11 9 8.47 8
10.84 12 9.13 12 8.15 12 7.04 8
4.26 4 3.1 4 5.39 4 5.25 8
4.82 7 7.26 7 6.42 7 12.5 19
8.33 11 9.26 11 7.81 11 5.56 8
7.58 13 8.74 13 12.74 13 7.91 8
7.24 6 6.13 6 6.08 6 6.89 8

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