Answer:
The correlation coefficient is 0.96
Step-by-step explanation:
The Given Table showing year and cost:
Year Cost
1948 0.36
1963 0.86
1974 1.89
1978 2.34
1985 3.55
1991 4.21
1997 4.59
2005 6.41
2010 7.89
Regression table:
Regression table can be made if we rewrite the year column by associating
1948 with 0, and the years after 1948 to be associated with the number of years after 1948. For example, if 1948 is associated with 0, then 1963 would come after 15 years, hence 1963 would be represented by 15, and with the same way, we can associate other years as well. Have a look:
Year (X) Cost (Y) X² XY
0 0.36 0 0
15 0.86 225 12.9
26 1.89 676 49.14
30 2.34 900 70.2
37 3.55 1369 131.35
43 4.21 1849 181.03
49 4.59 2401 224.91
57 6.41 3249 365.37
62 7.89 3844 489.18
∑X= 319 ∑Y= 32.1 ∑X²= 14513 ∑XY= 1524.08
As the correlation coefficient (r) can be determined as follows:
r = n (∑ XY) - (∑X) (∑Y) ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]
But, we need an additional column Y²
So,
Y²
0.1296
0.7396
3.5721
5.4756
12.6025
17.7241
21.0681
41.0881
62.2521
∑Y² = 164.6518
As,
r = n (∑ XY) - (∑X) (∑Y) ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]
So,
r = 9 (524.08) - (319)(32.1) ÷ √[9(14513 )-(319)²][9(164.6518)-(32.1)²]
[tex]r = \frac{3476.82}{\sqrt{(28856)(451.4562)}}[/tex]
[tex]r = \frac{3476.82}{\sqrt{(13027220.11)}}[/tex]
[tex]r = \frac{3476.82}{\sqrt{(3609.32)}} = 0.96[/tex]
So, the correlation coefficient is 0.96.
Keywords: correlation coefficient
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