8.8. Regressions in Imaginary Worlds: A Thought Experiment Imagine the following

Question

8.8. Regressions in Imaginary Worlds: A Thought Experiment Imagine the following world with very strict laws: Those with an eighth-grade education earn $10,000/annually. For every year of additional education, someone earns $5,000 more. The law does not allow any variation whatsoever. Everyone goes to school until at least eighth grade Researchers collect data on years of education and earnings from everyone in this imaginary world. They perform a regression of earnings on education (i.e., earnings is the dependent variable and education is the independent variable) and calculate the correlation between the two variables. Before continuing, try to answer these questions, explaining your answers What is the correlation coefficient? What is the R-squared of the regression? What is the regression coefficient of education? (Make sure to state its units)

Explanation / Answer

Here

The correlation coefficient is = R = 0.661

The R squared of the regression is R2 = 0.436

The regression coefficient of education = 3909.907

Interpretation:

a) For a unit increase in Educational level (years), earnings will increase 3909.907 unit.

b) When Educational level (years) = 0, earnings will be = -18331.178

c) 43.6% of variation in earnings will be explained by the above regression equation with predictor Educational level.

d) predicted salary = -18331.178 + (3909.907*12) = 28587.71

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