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Monthly Credit Card charges December   January 1545.24   903.07 4302.19   7208.16 4227.61   4242.62 202.81   79.93 3297.71   4046.26...

Spending on credit cards decreases after the Christmas spending season (as measured by amount charged on a credit card in Decc) Give a 95% confidence interval for the average January charges of cardholders who charged $2000 in December. ( $$ (Round t

Monthly Credit Card charges

December   January
1545.24   903.07
4302.19   7208.16
4227.61   4242.62
202.81   79.93
3297.71   4046.26
874.73   89.16
3810.51   3291.06
1935.26   2418.75
99.13   83.92
504.72   6.42
410.88   0.00
683.25   564.36
2159.04   2714.58
1123.46   187.11
2509.71   3268.75
1835.18   1523.58
9.95   1360.31
2334.13   732.98
78.55   75.13
101.29   70.22
598.12   633.81
648.44   1041.91
236.13   553.81
1265.72   1016.92
2124.07   1304.08
3.66   249.42
305.91   48.73
1902.23   871.78
559.02   485.04
2448.35   616.27
2799.41   1574.17
531.39   422.91
537.22   769.43
767.24   56.58
1960.36   1486.88
1678.03   495.83
2065.72   1065.31
396.98   509.98
5638.43   5642.07
5.49   5.49
2281.35   870.51
3820.83   1635.03
89.12   92.11
1452.02   669.24
527.51   829.42
105.82   69.17
1404.59   831.15
4230.41   2303.44
633.76   270.25
970.53   210.46
347.97   1011.22
0.00   1045.12
49.99   298.23
30.03   -30.03
471.71   1634.75
1116.85   1733.45
70.68   0.00
31.09   31.41
4.95   4.95
2521.25   1088.33
16.98   26.87
40.53   120.25
258.76   2009.24
122.96   291.37
0.00   104.07
109.85   53.03
5057.31   2839.77
3674.02   675.28
139.79   221.74
76.03   37.78
3150.77   533.34
2989.53   1934.23
651.22   693.13
9123.04   6804.04
916.57   393.25
2874.06   1307.14
796.93   796.71
34.58   0.00
44.15   1040.62
478.46   565.41
762.18   339.48
2351.16   5276.09
44.23   40.08
43.26   43.36
1340.74   652.81
1127.72   1071.79
2801.32   2336.48
52.14   91.53
1295.39   1433.79
328.67   719.61
28.34   28.62
598.55   980.86
4277.96   1577.65
567.55   0.00
479.26   161.93
1617.14   493.71
285.37   533.99
1285.69   462.06
3761.52   1477.76

Spending on credit cards decreases after the Christmas spending season (as measured by amount charged on a credit card in December). The accompanying data set contains the monthly credit card charges of a random sample of 99 cardholders. Complete parts a) through e) below. F: Click the icon to view the monthly credit card charges. a) Build a regression model to predict January spending from December's spending. Jan=+Dec (Round to four decimal places as needed.) Check the conditions for this model. Select all of the true statements related to checking the conditions. A. All of the conditions are definitely satisfied. B. The Equal Spread Condition is not satisfied. O C. The Randomization Condition is not satisfied OD. The Linearity Condition is not satisfied. E. The Nearly Normal Condition is not satisfied. b) How much, on average, will cardholders who charged $2000 in December charge in January? (Round to the nearest cent as needed.)
c) Give a 95% confidence interval for the average January charges of cardholders who charged $2000 in December. ( $$ (Round to the nearest cent as needed.) d) From part c), give a 95% confidence interval for the average decrease in the charges of cardholders who charged $2000 in December. (Round to the nearest cent as needed.) e) What reservations, if any, would a researcher have about the confidence intervals made in parts c) and d)? Select all that apply. A. The data are not independent, so the confidence intervals are not valid. OB. The data are not linear, so the confidence intervals are not valid. O C. The normal probability plot of the residuals shows curvilinear pattern, so the confidence intervals may not be valid. ND The residuals show increasing spread, so the confidence intervals may not be valid. E. A researcher would not have any reservations. The confidence intervals are valid.
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Answer #1

Excel output:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.784308036
R Square 0.615139095
Adjusted R Square 0.611171456
Standard Error 874.5508582
Observations 99
ANOVA
df SS MS F Significance F
Regression 1 118579989.3 118579989.3 155.0391 7.89731E-22
Residual 97 74189402.74 764839.2035
Total 98 192769392
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 120.7405259 115.5862952 1.044592057 0.298808 -108.6662742 350.1473259
December 0.699497556 0.056177909 12.45147019 7.9E-22 0.587999958 0.810995154

(a):~\widehat{Jan}=120.7405+0.6995Dec.

From probability plot, we see that normality assumption holds. From residual plot we see that as fitted value increases the absolute value of residual also increases. Hence the equal spread conditions are not satisfied.

Option: B.

(b):~When~Dec=2000,~then~\widehat{Jan}=120.7405+0.6995*2000=\$ 1519.74.

(c) Minitab output:

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 1519.74 95.5 (1330.24, 1709.24) (-226.32, 3265.79)

Answer: ($1330.24, $1709.24).

(d) Answer: (-$226.32, $3265.79)

(e) Option D.

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