Exercise 14-21 Algo A social scientist would like to analyze the relationship be

Question

Exercise 14-21 Algo A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual's annual salary (in $1,000s): Education Salary 36 43 63 48 59 38 104 49 a. Find the sample regression equation for the model: Salary = A + Education + . (Round intermediate calculations to at least 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.) Salary = Education b. Interpret the coefficient for Education. O As Education increases by 1 unit, an individual's annual salary is predicted to increase by $6,500. As Education inceases by 1 unit, an individua's annual salary is predicted to decrease by $7,500. OAs Education increases by 1 unit, an individual's annual salary is predicted to decrease by s6,soo. O As Education increases by 1 unit, an individual's annual salary is predicted to increase by $7,500. c. What is the predicted salary for an individual who completed 9 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.) Salary References eBook& Resources

Explanation / Answer

SolutiuonA:

PErform linear regression in R

lm function is used

y--salary

x--education

using summary we get the coefficients

education <- c(3,4,6,2,5,4,8,0)
salary <- c(36000,43000,63000,48000,59000,38000,104000,49000)
mod1 <- lm(salary~education)
summary(mod1)

Call:

lm(formula = salary ~ education)

Residuals:

Min 1Q Median 3Q Max

-17000 -12125 -3750 9500 23000

Coefficients:

Estimate Std. Error t value Pr(>|t|)  

(Intercept) 29000 11563 2.508 0.0460 *

education 6500 2508 2.591 0.0411 *

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16260 on 6 degrees of freedom

Multiple R-squared: 0.5281, Adjusted R-squared: 0.4495

F-statistic: 6.715 on 1 and 6 DF, p-value: 0.04114

salary=29000+6500(education)

Solutionb:

coefficient ofr education =slope=6500

slope=change in y/change in x=6500

change in salary/change in eductaion =6500

For unit Education salary increases by 6500

OPTIONA

Solutionc:

we have

salary=29000+6500(education)

for education=9

substitute in Regression Eq

=29000+6500*(9)

=87500

ANSWER:87500

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