Question

(e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. If required, round your answer to the nearest whole number. in the data set, which has 28 miles, and sells for $ 2 less than its predicted The best bargain is the Camry # price. in the data set, which has 47 miles, and sells for $ less than its The second best bargain is the Camry # predicted price.

Answer 1

X	Y	XY	X²	Y²
22	16.2	356.4	484	262.44
29	16	464	841	256
36	13.8	496.8	1296	190.44
47	11.5	540.5	2209	132.25
63	12.5	787.5	3969	156.25
77	12.9	993.3	5929	166.41
73	11.2	817.6	5329	125.44
87	13	1131	7569	169
92	11.8	1085.6	8464	139.24
101	10.8	1090.8	10201	116.64
110	8.3	913	12100	68.89
28	12.5	350	784	156.25
59	11.1	654.9	3481	123.21
68	15	1020	4624	225
68	12.2	829.6	4624	148.84
91	13	1183	8281	169
42	15.6	655.2	1764	243.36
65	12.7	825.5	4225	161.29
110	8.3	913	12100	68.89
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
1268	238.4	15107.7	98274	3078.84

Sample size, n =	19
x̅ = Ʃx/n = 1268/19 =	66.7368421
y̅ = Ʃy/n = 238.4/19 =	12.5473684
SSxx = Ʃx² - (Ʃx)²/n = 98274 - (1268)²/19 =	13651.6842
SSyy = Ʃy² - (Ʃy)²/n = 3078.84 - (238.4)²/19 =	87.5473684
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 15107.7 - (1268)(238.4)/19 =	-802.36316

Slope, b = SSxy/SSxx = -802.36316/13651.68421 =    -0.058773932

y-intercept, a = y̅ -b* x̅ = 12.54737 - (-0.05877)*66.73684 =    16.46975503

Regression equation :   

ŷ = 16.4698 + (-0.0588) x  

Predicted price and residual.

X	Y	Predicted value, ŷ	Residual, y-ŷ
22	16.2	16.4698 + (-0.0588) * 22 = 15.1767	1.0233
29	16	16.4698 + (-0.0588) * 29 = 14.7653	1.2347
36	13.8	16.4698 + (-0.0588) * 36 = 14.3539	-0.5539
47	11.5	16.4698 + (-0.0588) * 47 = 13.7074	-2.2074
63	12.5	16.4698 + (-0.0588) * 63 = 12.767	-0.2670
77	12.9	16.4698 + (-0.0588) * 77 = 11.9442	0.9558
73	11.2	16.4698 + (-0.0588) * 73 = 12.1793	-0.9793
87	13	16.4698 + (-0.0588) * 87 = 11.3564	1.6436
92	11.8	16.4698 + (-0.0588) * 92 = 11.0626	0.7374
101	10.8	16.4698 + (-0.0588) * 101 = 10.5336	0.2664
110	8.3	16.4698 + (-0.0588) * 110 = 10.0046	-1.7046
28	12.5	16.4698 + (-0.0588) * 28 = 14.8241	-2.3241
59	11.1	16.4698 + (-0.0588) * 59 = 13.0021	-1.9021
68	15	16.4698 + (-0.0588) * 68 = 12.4731	2.5269
68	12.2	16.4698 + (-0.0588) * 68 = 12.4731	-0.2731
91	13	16.4698 + (-0.0588) * 91 = 11.1213	1.8787
42	15.6	16.4698 + (-0.0588) * 42 = 14.0012	1.5988
65	12.7	16.4698 + (-0.0588) * 65 = 12.6494	0.0506
110	8.3	16.4698 + (-0.0588) * 110 = 10.0046	-1.7046

The best bargain is the Camry #12 in the data set, which has 28000 miles and sells for 2324 less than its predicted price.

The best bargain is the Camry #4 in the data set, which has 47000 miles and sells for 2207 less than its predicted price.