Question

In: Statistics and Probability

It appears that the imports of carbon black have been increasing by about 10% annually. Imports...

It appears that the imports of carbon black have been increasing by about 10% annually.

Imports of
Carbon Black
Year (thousands of tons)
2010 94
2011 109
2012 111
2013 127
2014 132
2015 145
2016 162
2017 178

Determine the logarithmic trend equation. (Round your answers to 4 decimal places.)

ŷ =    +    t, where 2010 is coded 1.

By what percent did imports increase, on the average, during the period? (Round your answer to 2 decimal places.)

Imports increased, on average: %

Estimate imports for the year 2023. (Round your intermediate calculations. Round your answer to 2 decimal places.)

Estimated Imports=

Solutions

Expert Solution

Input:

Year(x) Imports of Carbon Black(1000's of tons)(Y) ln(x)
1 94 0
2 109 0.693147
3 111 1.098612
4 127 1.386294
5 132 1.609438
6 145 1.791759
7 162 1.94591
8 178 2.079442

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.922409171
R Square 0.850838679
Adjusted R Square 0.825978458
Standard Error 11.82376626
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 4784.691309 4784.691309 34.2249051 0.001100904
Residual 6 838.8086912 139.8014485
Total 7 5623.5
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 82.97992484 9.40235289 8.825442505 0.000117545 59.97319613 105.9866536 59.97319613 105.9866536
ln(x) 37.16882234 6.353421595 5.85020556 0.001100904 21.62255975 52.71508493 21.62255975 52.71508493

Y = 82.9799+37.1688*ln(x)

Year(x) Imports of Carbon Black(1000's of tons)(Y) % increase
1 94 0.00%
2 109 15.96%
3 111 1.83%
4 127 14.41%
5 132 3.94%
6 145 9.85%
7 162 11.72%
8 178 9.88%
Average 8.45%

For Year 2023, X = 2023-2010+1 = 14

Y = 82.9799+37.1688*ln(x)

Y = 82.9799+37.1688*ln(14) = 181.07

Estimated Imports = 181.07


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