Question

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.)

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

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): Jan = 120.7405 +0.6995 Dec.

Residual Plots for January Normal Probability Plot Versus Fits 99.9 99 4000 90 2000 Per cent 50 Residual 0 10 1 0.1 -2000 -2000 0 2000 4000 0 1500 6000 Residual 3000 4500 Fitted Value Histogram Versus Order 40 4000 30 2000 Frequency 20 10 -2000 -2000-1000 0 3000 4000 90 1000 2000 Residual 1 10 20 30 40 50 60 70 80 Observation Order

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.