2. Suppose you are interested in the relationship between weekly wage earnings i
ID: 3375438 • Letter: 2
Question
2. Suppose you are interested in the relationship between weekly wage earnings in do lars) and age (in years). You run a linear regression model where age is your dependent variable and earn is your independent variable. Answer the following questions about your regression results. earn = 239.16 + 5.20 × age (20.24) (0.57) R2 = 0.05, S E R = 287.21 (b) Is the effect of age on earnings economically significant here? (Hint: think about (c) The average age in this sample is 37.5 years. What is the average yearly earning (a) Interpret the coefficient for age. how much does a person earn more in a year as age increases by 1 year) in the sample? (d) Interpret R2 and state the unit for SER. (e) Is age statistically significant? Conclude by computing t statistic and p-value. (f) You hypothesize that age should be positively affecting earnings. Conduct this one sided test and conclude.Explanation / Answer
(a) The coefficient for age is 5.20.This figure shows that predicted earnings increase by 5.20 dollars for a unit increase in age.Here the inference that the earnings increases with increase in age is supported by the positive sign of the regression coefficient value (i.e, + 5.20)
(b) The effect of age on earnings may however be not economically significant.Since the earnings usually increase with age only if 'experience in work','required skill updates',improved performance;' and 'age' go hand in hand.
(c) Given average age = 37.5, then
Average yearly earnings = 239.16 + 5.20 * 37.5 = 434.16 dollars.
(d) Here, the coffecient of determinaton R2 = 0.05.It implies only 5% variation in the earnings of an individual is expained by his age.Hence the model is not statistically significant.
The unit for SER is that of the response variable, here, dollars.
(e) t statistic for age:
tage = estimated regression coefficient / Corresponding standard error
= 5.20 / 0.57
= 9.123
The significance of this value can be tested for given degrees of freedom (df) and the corresponding p value can be generated.If the no. of observations (n) are available for the given data, then its df = n-1.Look for t value corresponding to (n-1) df in t tables for a specific level of significanc, usually 5% or 1%.
If 9.123 is greater than the tabled t value, we may conclude that age, here, is statistically significant.
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