Estimate: Wage = 0 + 1 EDUC + 2 EXPER + 3 AGE + . (Negative values should be ind

Question

Estimate: Wage = 0 + 1EDUC + 2EXPER + 3AGE + . (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Predict the hourly wage of a 40-year-old employee who has 5 years of higher education and 8 years of experience. (Round intermediate coefficient values and final answer to 2 decimal places.)

eBook & Resources

eBook: Calculate and interpret the coefficient of determination, R2

A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE).

Explanation / Answer

Lets analyse this in the open source statistical pakage R , the snippet is as follows

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\wage.csv",header=TRUE)
str(data.df)

## fit the model

model<- lm(Wage~.,data=data.df)

summary(model)

The results are

> summary(model)

Call:
lm(formula = Wage ~ ., data = data.df)

Residuals:
Min 1Q Median 3Q Max
-9.4012 -3.0362 -0.6326 2.4952 15.1513

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 8.67688 4.07963 2.127 0.03895 *
EDUC 1.23076 0.36438 3.378 0.00152 **
EXPER 0.42394 0.14129 3.001 0.00438 **
AGE -0.02212 0.08282 -0.267 0.79059   
Gender 2.37744 1.65706 1.435 0.15828   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.351 on 45 degrees of freedom
Multiple R-squared: 0.3711,   Adjusted R-squared: 0.3152
F-statistic: 6.639 on 4 and 45 DF, p-value: 0.0002744

the coefficients are

model$coefficients
(Intercept) EDUC EXPER AGE Gender
8.6768754 1.2307643 0.4239350 -0.0221226 2.3774441

yes , as education increases wages also increases - positive relationship

yes , as experience increases wages also increases - positive relationship

yes, as age increases wages might decrease a bit , assuming that the productivity decreases of the employee

Gender : this tells us that males tend to earn higher than females (assuming 0 is females , else reverse the results if 0 = males)

c) correct answer is

For a 1 year increase in higher education, wage is predicted to increase by $1.44/hour holding experience and age constant. though we get the coefficient as 1.24 and not 1.44

d) Multiple R-squared: 0.3711 is the coefficient of determination. This tells us the variation of the data captured by the model . Hence the closest answers are

34.24% of the sample variation in wage is explained by the estimated regression model.

Please note that the answer choices are different from the absolute results we see. However , we are sure that the results obtained from R software are correct.

using the equation

model$coefficients
(Intercept) EDUC EXPER AGE Gender
8.6768754 1.2307643 0.4239350 -0.0221226 2.3774441

and putting the values

8.67 + 1.23*5 + 0.423*8 - 0.02*40 + 0 = 17.4

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