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# Correlation Testing & Regression Analysis

The Mauna Loa Observatory at 11,000 feet elevation in the middle of the Pacific Ocean sits in a prime spot for measuring carbon dioxide levels in the atmosphere without local contamination. Operated by the National Oceanic and Atmospheric Administration's Climate Monitoring and Diagnostics Laboratory, the observatory has been measuring CO2 levels (in parts per million) since 1958. Below is a table of CO2 levels since 1975.

Use as x Use as y
Years since 1975 Year CO2 Level
0 1975 331
5 1980 339
10 1985 346
15 1990 354
20 1995 361
25 2000 369

a) Use a 0.05 significance level to test for a linear correlation between years since 1975 and CO2 level.
b) What percentage of the variation in the CO2 level can be explained by the linear relationship between the CO2 level and years since 1975? 95%?
c) Find the equation of the regression line that expresses CO2 level (y) in terms of years since 1975 (x).
d) Use your equation to estimate the CO2 level in the year 2020.

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for significance of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.

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