In: Statistics and Probability
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.)
|
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=
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