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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 97 2011 108 2012 111 2013 128 2014 135 2015 144 2016 166 2017 178 Click here for the Excel Data File 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.) Estimate imports for the year 2023. (Round your intermediate calculations. Round your answer to 2 decimal places.)

Solutions

Expert Solution

year Imports ln x
2010 97 7.60589
2011 108 7.606387
2012 111 7.606885
2013 128 7.607381
2014 135 7.607878
2015 144 7.608374
2016 166 7.608871
2017 178 7.609367
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.98681288
R Square 0.97379966
Adjusted R Square 0.969432937
Standard Error 4.974941382
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 5519.374749 5519.374749 223.0046642 5.67655E-06
Residual 6 148.5002505 24.75004176
Total 7 5667.875
Coefficients Standard Error t Stat P-value Lower 95%
Intercept -175465.1562 11758.82455 -14.921998 5.70189E-06 -204237.9634
ln x 23081.89952 1545.662153 14.93334069 5.67655E-06 19299.80048

y^= -175465.1562 + 23081.8995 ln(year)

for year = 2023

y^=

242.0377589

orchestra answered 2 years ago
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