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Variable to Predict Amounts of Depositions for the British Bank

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1. (2.5 points) The British Bankers' Association decided to look at a variable to predict amounts of deposits. It chose the number of branches for each bank. The data are:

Bank Name Deposits (£ billion) Branches in 2006
Abbey National 101.7 867
Barclays 108.2 1997
Lloyds 96.9 2797
National Westminster 113.8 1920
Woolrich 27.5 430
Halifax 77.1 938

Results of SLR model analysis of the data include:

? The regression model is = 51.97 +0.024X
? The t-test statistic for Branches is 1.775 and the p-value is 0.1505
? R2 for this model is 44%

(a) At the 5% level, is the model statistically significant?

(b) What does the R2 mean?

(c) Suppose Roberts Bank was also a member of the British Bankers' Association and had 600 branches in 2006. Could you use this model to predict the amount of deposits in Roberts Bank? If so, what would your prediction be?

(d) Suppose they built a second SLR model, this time looking at the number of customers at each bank to predict deposits, with R2 for this model equal to 75%. Which variable do you think is more strongly related to deposits? Why?

2. (2.5 points) Quarterly sales for the Hudson Marine Co. for the past seven years are:

Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4 Total
Yearly Sales
1 6 15 10 4 35
2 10 18 15 7 50
3 14 26 23 12 75
4 19 28 25 18 90
5 22 34 28 21 105
6 24 36 30 20 110
7 28 40 35 27 130

Seasonal indices (indexes) for the four quarters are:

Quarter Index
1 0.899
2 1.362
3 1.118
4 0.621

(a) When does Hudson Marine Co. experience the greatest seasonal effect? Does this seem reasonable? Explain.

(b) The trend equation of deseasonalized sales is = 6.332 +1.055 tcoded with R2 = 0.89 What are the forecasts for the four quarters of this year (year eight)?

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The solution examines the research for the British Bankers Association.

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