Math Problem Statement

In this​ exercise, you will investigate the relationship between a​ worker's age and earnings.​ (Generally, older workers have more job​ experience, leading to higher productivity and​ earnings.) The following table contains data -

College Distance Ahe Age 16.34615326 31 37.0370369 27 26.44230843 34 15.86538506 26 11.5 26 16.82692337 26 9.791666985 30 11 28 30.76922989 29 24.03846169 25 10.6275301 28 23.41346169 33 15.59251595 31 25.64102554 27 8.241758347 34 39.90384674 33 13.46153831 27 15.38461494 32 19.23077011 27 19.23077011 25 12.98076916 30 8.653845787 32 21.63461494 34 12.5 31 17.94871712 33 24.61538506 31 13.15789509 30 10.57692337 25 26.44230843 28 7.692307472 30 24.03846169 31 21.63461494 33 14.66346169 30 33.65384674 28 25.96153831 31 7.692307472 26 15.38461494 28 15.38461494 30 19.23077011 30 12.01923084 33 9.616346359 32 19.23077011 33 23.07692337 34 17.78846169 27 7.211538315 25 14.42307663 30 29.12087822 30 9.134614944 34 17.09401703 30 12.5 30 7.211538315 33 21.63461494 30 17.38461494 30 14.42307663 25 4.945055008 33 12.06140327 25 19.23077011 26 5.341880322 28 21.63461494 26 9.615385056 26 20.67307663 33 16.82692337 34 7.692307472 26 15.625 29 23.07692337 32 6.025640965 32 14.42307663 33 18.84615326 27 13.94230747 25 66.82691956 33 16.34615326 32 39.90384674 31 5.439005375 29 23.07692337 32 14.42307663 27 15.86538506 34 18.46230698 25 12.5 33 18.80341911 30 9.134614944 27 9.79020977 33 8.241758347 28 9.226190567 34 36.05769348 30 7.875 28 33.65384674 30 4.807692528 29 24.23077011 33 14.42307663 31 9.230769157 30 27.5 27 9.588461876 28 30 34 8.653845787 27 12.5 25 12.01923084 33 5.769230843 25 12.74509811 33 12.01923084 32 8.17307663 34

for​ full-time, full-years​ workers, age​ 25-34, with a high school diploma or​ B.A./B.S. as their highest degree. Download the data from the table by clicking the download table icon . A detailed description of the variables used in the dataset is available here LOADING... . Use a statistical package of your choice to answer the following questions. Part 2 Suppose you are interested in estimating the following model Ahe​ = beta 0β0 ​+ beta 1β1Age ​+ u Run a regression of average hourly earnings ​(AHE​) on age ​(Age​). Part 3 What is the estimated intercept ModifyingAbove beta with caret 0β0​? The estimated intercept ModifyingAbove beta with caret 0β0 is 3.31893.3189. ​(Round your response to four decimal places​) Part 4 What is the estimated slope ModifyingAbove beta with caret 1β1​? The estimated slope ModifyingAbove beta with caret 1β1 is enter your response here. ​(Round your response to four decimal places​)

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Statistics
Econometrics

Formulas

AHE = β0 + β1 * Age + u
Slope (β1) = (Σ(x_i - x̄) * (y_i - ȳ)) / (Σ(x_i - x̄)^2)

Theorems

Least Squares Estimation
Linear Model Assumptions

Suitable Grade Level

Undergraduate Economics or Statistics