2. Use the regression tool in Data Analysis to develop a regression model using
ID: 1116003 • Letter: 2
Question
2. Use the regression tool in Data Analysis to develop a regression model using account balance as the dependent variable and ATM use per month as the independent variable.
a) What is the coefficient on the independent variable? Interpret this in your own words.
b) Is this statistically significant at the 95% level? How do you know?
c) Predict the customer’s account balance if they use the ATM 5 times per month.
DATA to use:
Acct. Bal. # ATM tran. # services Debit card? Interest? City 1756 13 4 0 1 2 748 9 2 1 0 1 1501 10 1 0 0 1 1831 10 4 0 1 3 1622 14 6 0 1 4 1886 17 3 0 1 1 740 6 3 0 0 3 1593 10 8 1 0 1 1169 6 4 0 0 4 2125 18 6 0 0 2 1554 12 6 1 0 3 1474 12 7 1 0 1 1913 6 5 0 0 1 1218 10 3 1 0 1 1006 12 4 0 0 1 2215 20 3 1 0 4 137 7 2 0 0 3 167 5 4 0 0 4 343 7 2 0 0 1 2557 20 7 1 0 4 2276 15 4 1 0 3 1494 11 2 0 1 1 2144 17 3 0 0 3 1995 10 7 0 0 2 1053 8 4 1 0 3 1526 8 4 0 1 2 1120 8 6 1 0 3 1838 7 5 1 1 3 1746 11 2 0 0 2 1616 10 4 1 1 2 1958 6 2 1 0 2 634 2 7 1 0 4 580 4 1 0 0 1 1320 4 5 1 0 1 1675 6 7 1 0 2 789 8 4 0 0 4 1735 12 7 0 1 3 1784 11 5 0 0 1 1326 16 8 0 0 3 2051 14 4 1 0 4 1044 7 5 1 0 1 1885 10 6 1 1 2 1790 11 4 0 1 3 765 4 3 0 0 4 1645 6 9 0 1 4 32 2 0 0 0 3 1266 11 7 0 0 4 890 7 1 0 1 1 2204 14 5 0 0 2 2409 16 8 0 0 2 1338 14 4 1 0 2 2076 12 5 1 0 2 1708 13 3 1 0 1 2138 18 5 0 1 4 2375 12 4 0 0 2 1455 9 5 1 1 3 1487 8 4 1 0 4 1125 6 4 1 0 2 1989 12 3 0 1 2 2156 14 5 1 0 2 Column Full variable name A Account balance in $ B Number of ATM transactions last month C Number of other bank services used D Has a debit card (1 = yes, 0 = no) E Receives interest on the account (1 = yes, 0 = no) F Where banking is done 1 = Utica 2 = Schenectady 3 = Amsterdam 4 = RomeExplanation / Answer
Answer:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.7089
R Square
0.502539
Adjusted R Square
0.493962
Standard Error
424.6162
Observations
60
ANOVA
df
SS
MS
F
Significance F
Regression
1
10564096
10564096
58.59211781
2.33E-10
Residual
58
10457337
180298.9
Total
59
21021433
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
485.2097
143.4437
3.38258
0.001291648
198.076
772.3435
198.076
772.3435
ATM
98.51038
12.86952
7.654549
0.000000000233
72.74923
124.2715
72.74923
124.2715
a) Regression :
CAB = 485.2+98.51ATM
b) the p-value is very small =0.00 also the t value is >3 therefore otright rejected at all levels of significance. The 95% confidence interval also contains the value of ATMcoefficient therefore statistically significant.
c) AT ATM = 5
CAB = 485.2+98.51*5
CAB = 977.75
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.7089
R Square
0.502539
Adjusted R Square
0.493962
Standard Error
424.6162
Observations
60
ANOVA
df
SS
MS
F
Significance F
Regression
1
10564096
10564096
58.59211781
2.33E-10
Residual
58
10457337
180298.9
Total
59
21021433
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
485.2097
143.4437
3.38258
0.001291648
198.076
772.3435
198.076
772.3435
ATM
98.51038
12.86952
7.654549
0.000000000233
72.74923
124.2715
72.74923
124.2715
a) Regression :
CAB = 485.2+98.51ATM
b) the p-value is very small =0.00 also the t value is >3 therefore otright rejected at all levels of significance. The 95% confidence interval also contains the value of ATMcoefficient therefore statistically significant.
c) AT ATM = 5
CAB = 485.2+98.51*5
CAB = 977.75
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