Concept explainers
To find the least square regression line for the given data
Answer to Problem 2CS
Least square regression line is
Explanation of Solution
Given:
The inflation rate and the unemployment rate, both in percent, for the years 1988-2015 is as shown below.
Year | Inflation | Unemployment |
1988 | 4.4 | 5.5 |
1989 | 4.6 | 5.3 |
1990 | 6.1 | 5.6 |
1991 | 3.1 | 6.8 |
1992 | 2.9 | 7.5 |
1993 | 2.7 | 6.9 |
1994 | 2.7 | 6.1 |
1995 | 2.5 | 5.6 |
1996 | 3.3 | 5.4 |
1997 | 1.7 | 4.9 |
1998 | 1.6 | 4.5 |
1999 | 2.7 | 4.2 |
2000 | 3.4 | 4.0 |
2001 | 1.6 | 4.7 |
2002 | 2.4 | 5.8 |
2003 | 1.9 | 6.0 |
2004 | 3.3 | 5.5 |
2005 | 3.4 | 5.1 |
2006 | 2.5 | 4.6 |
2007 | 4.1 | 4.6 |
2008 | 0.1 | 5.8 |
2009 | 2.7 | 9.3 |
2010 | 1.5 | 9.6 |
2011 | 3.0 | 8.9 |
2012 | 1.7 | 8.1 |
2013 | 1.5 | 7.4 |
2014 | 0.8 | 6.2 |
2015 | 0.7 | 5.3 |
Concept used:
Given ordered pairs
First we find the sample means
Now to find standard deviations, we construct the table as shown below:
4.4 | 5.5 | 3.227157 | 0.294693 |
4.6 | 5.3 | 3.985728 | 0.551836 |
6.1 | 5.6 | 12.225015 | 0.196122 |
3.1 | 6.8 | 0.246441 | 0.573265 |
2.9 | 7.5 | 0.087870 | 2.123265 |
2.7 | 6.9 | 0.009298 | 0.734694 |
2.7 | 6.1 | 0.009298 | 0.003265 |
2.5 | 5.6 | 0.010726 | 0.196122 |
3.3 | 5.4 | 0.485013 | 0.413265 |
1.7 | 4.9 | 0.816440 | 1.306122 |
1.6 | 4.5 | 1.007154 | 2.380407 |
2.7 | 4.2 | 0.009298 | 3.396121 |
3.4 | 4.0 | 0.634299 | 4.173264 |
1.6 | 4.7 | 1.007154 | 1.803264 |
2.4 | 5.8 | 0.041441 | 0.058979 |
1.9 | 6.0 | 0.495012 | 0.001836 |
3.3 | 5.5 | 0.485013 | 0.294693 |
3.4 | 5.1 | 0.634299 | 0.888979 |
2.5 | 4.6 | 0.010726 | 2.081836 |
4.1 | 4.6 | 2.239299 | 2.081836 |
0.1 | 5.8 | 6.267867 | 0.058979 |
2.7 | 9.3 | 0.009298 | 10.608980 |
1.5 | 9.6 | 1.217868 | 12.653266 |
3.0 | 8.9 | 0.157155 | 8.163266 |
1.7 | 8.1 | 0.816440 | 4.231837 |
1.5 | 7.4 | 1.217868 | 1.841837 |
0.8 | 6.2 | 3.252868 | 0.024693 |
0.7 | 5.3 | 3.623582 | 0.551836 |
Therefore, standard deviations are,
Now to find correlation coefficient, we construct the table as shown below:
4.4 | 5.5 | 1.4036794 | ||
4.6 | 5.3 | 1.5599538 | ||
6.1 | 5.6 | 2.7320120 | ||
3.1 | 6.8 | 0.3878957 | 0.5009216 | 0.1943053 |
2.9 | 7.5 | 0.2316213 | 0.9640377 | 0.2232916 |
2.7 | 6.9 | 0.0753469 | 0.5670810 | 0.0427277 |
2.7 | 6.1 | 0.0753469 | 0.0378054 | 0.0028485 |
2.5 | 5.6 | 0.0237110 | ||
3.3 | 5.4 | 0.5441701 | ||
1.7 | 4.9 | 0.5338310 | ||
1.6 | 4.5 | 0.8004302 | ||
2.7 | 4.2 | 0.0753469 | ||
3.4 | 4.0 | 0.6223073 | ||
1.6 | 4.7 | 0.6966707 | ||
2.4 | 5.8 | 0.0255573 | ||
1.9 | 6.0 | 0.0155875 | ||
3.3 | 5.5 | 0.5441701 | ||
3.4 | 5.1 | 0.6223073 | ||
2.5 | 4.6 | 0.0772521 | ||
4.1 | 4.6 | 1.1692678 | ||
0.1 | 5.8 | 0.3143114 | ||
2.7 | 9.3 | 0.0753469 | 2.1549077 | 0.1623656 |
1.5 | 9.6 | 2.3533860 | ||
3.0 | 8.9 | 0.3097585 | 1.8902699 | 0.5855271 |
1.7 | 8.1 | 1.3609943 | ||
1.5 | 7.4 | 0.8978782 | ||
0.8 | 6.2 | 0.1039649 | ||
0.7 | 5.3 | 0.7310111 | ||
= |
Therefore,
Henceleast squares regression line is,
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Chapter 4 Solutions
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