A simple linear regression model for salary (Y) and the number of years of worki

Question

A simple linear regression model for salary (Y) and the number of years of working (Xi) is as follows: Yi-po + 1 Xi + ei where 0 and 1 are unknown parameters, and ei is the disturbance term The regression results are: Coefficient Intercept Working years B Standard error t Stat 5.00 10.00 20.00 0.50 value 0.005 0.001 Regression Statistics R Squared Standard error 9.4531 Observations 25 0.8643 a. Calculate the values of A and B. Explain. b. Explain the meaning of R Squared c. What conclusions can you reach about the relationships between salary (Yi) and working years (X)? What is the predicted salary for a person with 10 years working experience? Is this prediction reliable? d. e.

Explanation / Answer

A)

B)

R^2= 86.43%

There is 86.43% variation in dependent variable (salary) which is explained by independent variable (number of working years)

C)

with one year incrrease in working year there is $5 increase in salary.

D)

when x = 10

yhat = 100+5*x = 100+5*10 = 150

E)

i can say that prediction based on this model is reliable as R^2 is greater than 70% indicating model is a good fit to the data.

also, low value of Standard error tells us that model is reliable. and thus the predictions based on this model is also reliable.

coefficient SE t beta = t*SE intercept =5*20 100 20 5 working years =10*0.5 5 0.5 10

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