A national trade association is concerned with increasing competition from foreign companies. They decide, in close consultation with their membership, to evaluate the sales performance of 25 randomly selected U.S. companies, so that all companies can benefit from their collective experience.
The associationâ??s research director, with substantial input from member companiesâ?? sales managers, has decided to measure the performance, y, of each company by using the yearly sales of the same product for all of the companies.
The research director and the sales managers believe that sales performance, y (measured in hundreds of units), substantially depends on three independent variables:
x1 = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)
x2 = weighted average of the companyâ??s market share over the previous four years (Market Share)
x3 = change in the companyâ??s market share over the previous four years (Market share Change)
Refer to the Minitab output below to answer questions A through G.
Multiple Regression and Model Building: Minitab Output
Term Coef SE Coef T P 95% CI
Constant 1060.13 643.589 1.64722 0.114 (-278.284, 2398.55)
Advertising, x1 0.19 0.079 2.36297 0.028 (0.022, 0.35)
Market Share, x2 189.56 80.646 2.35057 0.029 (21.852, 357.28)
Market share Change, x3 664.45 332.514 1.99828 0.059 (-27.046, 1355.96)
Summary of Model
S = 937.108 R-Sq = 55.43% R-Sq(adj) = 49.07%
PRESS = 25785590 R-Sq(pred) = 37.69%
Analysis of Variance
Error Source DF Seq SS Adj SS Adj MS F
Regression 3 22937954 22937954 7645985 8.70671
Advertising, x1 1 14707456 4903392 4903392 5.58364
Market Share, x2 1 4723868 4852050 4852050 5.52518
Market share Change, x3 1 3506630 3506630 3506630 3.99311
Total 21 18441595 18441595 878171
Error 24 41379549
Advertising, x1 0.0278536
Market Share, x2 0.0285936
Market share Change, x3 0.0588001
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 4438.70 301.701 (3811.28, 5066.12) (2391.37, 6486.03)
Values of Predictors for New Observations
New Obs Advertising, x1 Market Share, x2 Market Share Change, X3
1 7281.65 9.64 0.28
Analyze the above output to determine the multiple regression equation. (5 points)
What conclusions are possible using the result of the global usefulness test (the F test and its associated p-value)? (5 points)
What conclusions are possible using the results of the t-tests of the independent variables (alpha = 0.10). Does this data provide significant evidence that Sales are associated with Time With Product and/or Market Potential and/or Advertising? Find the p-values and interpret. Interpret the 95% confidence interval of each of the regression coefficients, using the units of the variables. (20 points)
Find and interpret the 95% Prediction interval for Sales, when Advertising = 7281.65, Market Share = 9.64, and Market share Change = 0.28. (10 points)
(Points : 40)
Step by step method for regression analysis in Minitab is given in the answer.
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:
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