Linear Functions Worksheet Page 26
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38Section 1.3
The Least Squares Line
81
P
P
P
P
P
P
n(
xy) ¡ (
x)(
y)
n(
xy) ¡ (
x)(
y)
P
P
P
P
m =
m =
n(
x
2
) ¡ (
x)
2
n(
x
2
) ¡ (
x)
2
5(77:36) ¡ (13:9)(19:6)
15(20,127.47) ¡ (1200:6)(249:8)
=
=
5(53:07) ¡ 13:9
2
15(96,725.86) ¡ 1200:6
2
= 1:585250901 ¼ 1:585
= 0:211925009 ¼ 0:212
P
P
y ¡ m(
x)
b =
n
P
P
y ¡ m(
x)
249:8 ¡ 0:212(1200:6)
b =
=
n
15
19:6 ¡ 1:585250901(13:9)
=
¼ ¡0:315
5
Y = 0:212x ¡ 0:315
¼ ¡0:487
Y = 1:585x ¡ 0:487
(b) Let x = 73; …nd Y:
Y = 0:212(73) ¡ 0:315
¼ 15:2
±
If the temperature were 73
F, you would
expect to hear 15.2 chirps per second.
(c) Let Y = 18; …nd x:
18 = 0:212x ¡ 0:315
18:315 = 0:212x
86:4 ¼ x
When the crickets are chirping 18 times
(c) No, it gives negative values for small widths.
±
per second, the temperature is 86.4
F.
5(77.36) ¡ (13:9)(19:6)
(d) r =
p
p
5(53.07)¡13:9
2
¢
5(113:18)¡19:6
2
(d)
¼ 0:999
15(20,127) ¡ (1200:6)(249:8)
p
p
r =
2
2
x
y
xy
x
y
15(96,725.86)¡(1200:6)
2
¢
15(4200:56)¡(249:8)
2
13. (a)
88:6
20:0
1772
7849:96
400:0
= 0:835
71:6
16:0
1145:6
5126:56
256:0
93:3
19:8
1847:34
8704:89
392:04
84:3
18:4
1551:12
7106:49
338:56
2
2
x
y
xy
x
y
80:6
17:1
1378:26
6496:36
292:41
14. (a)
5
25
75:2
15:5
1165:6
5655:04
240:25
26.9
134.5
723.61
10
258:0
100
69:7
14:7
1024:59
4858:09
216:09
25.8
665.64
15
370:5
225
82:0
17:1
1402:2
6724
292:41
24.7
610.09
20
446:0
69:4
15:4
1068:76
4816:36
237:16
22.3
400
497.29
30
561:0
900
83:3
16:2
1349:46
6938:89
262:44
18.7
349.69
35
626:5
1225
79:6
15:0
1194
6336:16 225
17.9
320.41
40
688:0
1600
82:6
17:2
1420:72
6822:76
295:84
17.2
295.84
45
778:5
2025
80:6
16:0
1289:6
6496:36
256:0
17.3
299.29
50
2500
83:5
17:0
1419:5
6972:25
289:0
16.0
800:0
256.00
55
852:5
3025
76:3
14:4
1098:72
5821:69
207:36
15.5
240.25
305
5515:5
1200:6
249:8 20,127.47 96,725.86 4200:56
202.3
12,025
4258.11
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