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.

December	January
1544.27	904.12
4296.56	7206.67
4231.61	4242.12
202.81	79.91
3298.24	4043.64
873.19	89.18
3810.19	3291.88
1933.67	2419.82
99.18	83.85
504.04	6.42
410.81	0.00
682.61	564.18
2161.39	2716.61
1123.94	187.14
2508.91	3268.47
1836.74	1524.15
9.95	1359.21
2335.77	733.37
78.61	75.02
101.37	70.29
598.63	633.69
648.99	1041.04
236.05	553.21
1266.11	1016.51
2122.66	1305.29
3.66	249.69
306.01	48.77
1902.62	872.67
559.31	485.47
2444.42	617.16
2802.07	1574.73
531.66	422.77
536.63	769.55
767.15	56.59
1957.22	1485.88
1677.47	495.22
2062.16	1064.18
397.01	510.68
5637.73	5640.54
5.49	5.49
2277.97	871.06
3817.64	1635.57
89.26	92.28
1452.86	669.77
527.62	829.52
105.78	69.26
1404.26	830.73
4232.29	2301.53
633.05	270.29
971.17	210.29
348.26	1011.77
0.00	1044.75
49.98	298.69
30.02	-29.98
472.03	1636.92
1115.27	1731.36
70.74	0.00
31.09	31.38
4.95	4.95
2523.34	1087.29
16.97	26.86
40.55	120.25
258.99	2007.56
122.88	291.58
0.00	104.07
109.79	53.01
5052.02	2841.17
3675.97	674.71
139.71	221.77
76.03	37.75
3153.81	533.38
2988.82	1931.72
651.65	692.13
9125.53	6804.52
916.77	392.98
2874.47	1307.01
798.29	796.03
34.57	0.00
44.17	1039.59
478.15	564.94
762.55	339.55
2349.89	5279.32
44.24	40.07
43.32	43.36
1339.63	653.94
1128.86	1070.82
2800.39	2334.09
52.16	91.46
1294.96	1435.03
328.42	719.74
28.34	28.59
599.23	980.01
4279.28	1576.48
567.56	0.00
479.95	161.82
1617.29	494.08
285.68	533.44
1283.56	462.02
3756.93	1479.44

​a) Build a regression model to predict January spending from​ December's spending.

Jan with caret=____+____Dec ​(Round to four decimal places as​ needed.)

​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.)

Answer 1

Ʃx =	132265.87
Ʃy =	104476.9
Ʃxy =	309071548.2
Ʃx² =	419022639.3
Ʃy² =	303006428.9
Sample size, n =	99
x̅ = Ʃx/n = 132265.87/99 =	1336.018889
y̅ = Ʃy/n = 104476.9/99 =	1055.322222
SSxx = Ʃx² - (Ʃx)²/n = 419022639.3379 - (132265.87)²/99 =	242312938.7
SSyy = Ʃy² - (Ʃy)²/n = 303006428.9386 - (104476.9)²/99 =	192749634.7
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 309071548.2037 - (132265.87)(104476.9)/99 =	169488436.4

a)

Slope, b = SSxy/SSxx = 169488436.35114/242312938.66258 = 0.6994609

y-intercept, a = y̅ -b* x̅ = 1055.32222 - (0.69946)*1336.01889 = 120.82919

Regression equation :

ŷ = 120.8292 + (0.6995) x

b) Predicted value of y at x = 2000

ŷ = 120.8292 + (0.6995) * 2000 = 1519.75

c)  Significance level, α = 0.05

Critical value, t_c = T.INV.2T(0.05, 97) = 1.9847  

Sum of Square error, SSE = SSyy -SSxy²/SSxx

= 192749634.65971 - (169488436.35114)²/242312938.66258 =    74199093.3

Standard error, se = √(SSE/(n-2)) = √(74199093.30064/(99-2)) =    874.60797

95% confidence interval:

d) 95% confidence interval: