Suppose that a random sample of 200 40-year old men is selected from a populatio

Question

Suppose that a random sample of 200 40-year old men is selected from a population and the annual income of each man is recorded. Suppose I am also able to obtain the annual income of each man's father when the father was 40. A regression of the former on the latter yields 1. We25+0.5W where W and W are the annual income in thousands of dollars of man i and his father, respectively, both measured in 1980 dollars (i) Explain what the estimates (25 for the intercept and 0.5 for the slope) mean intuitively. (ii) What is the predicted annual income for someone whose father earned $50,000? iii) Using the estimates from this regression, what is the effect of a $20, 000 increase in the income of the father on the son's earnings? (iv) Discuss the validity of the three least squares assumptions in this example. (v) I can convert the data to 2013 dollars by multiplying by 2.83. How would the estimates of the slope and intercept change? What if I convert only the son's income to 2013 dollars?

Explanation / Answer

i)
here intercept is 25
which means whose father at age 40 earning was 0 , their income is 25000 $ now
slope is 0.5 , which means
on average when father's income age increase by 1000 $, then annual income increase by 500 $ now

ii)
25 + 0.5 * 50
= 25 + 25
= 50

iii)

when increase in 20000
then son's income increase by 0.5*20000
= 10000 increase

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