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Regression analysis using MINITAB

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According to the Capital Asset Pricing Model (CAPM), the risk associated with a capital asset is proportional to the slope ß obtained by regressing the asset's past returns with the corresponding returns of the average portfolio called the market portfolio. (The return of the market portfolio represents the return earned by the average investor. It is a weighted average of the returns from all of the assets in the market.) The larger the slope ß of an asset, the larger is the risk associated with that asset. A ß of 1.00 represents average risk.
The returns from an electronic firms stock and the corresponding returns for the market portfolio for the past 15 years are given below.
Market Return % Stock's Return %
16.02 21.05
12.17 17.25
11.48 13.1
17.62 18.23
20.01 21.52
14 13.26
13.22 15.84
17.79 22.18
15.46 16.26
8.09 5.64
11 10.55
18.52 17.86
14.05 12.75
8.79 9.13
11.6 13.87

1. Carry out the regression and find the ß for the stock. What is the regression equation?
(Templates are attached if they can be used)

2. Does the value of the slope indicate that the stock has above-average risk? (For the purposes of this case, assume that the risk is average if the slope is in the range 1 ± 0.1, below average if it is less than 0.9, and above average if it is more than 1.1)
3. (Templates are attached if they can be used)

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Solution Summary

This solution uses MINITAB to do a regression analysis and interprets the output.

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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 α = 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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