Question 6 A state official was investigating the relationship between salary (x

Question

Question 6 A state official was investigating the relationship between salary (x) and the number of absences (y) for state employees. The variable y in the following table represents the average number of absences per year for employees at that salary x Eploye bsences Salary (x) in thousands 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 2.3 2.0 2.0 4 2.2 1.5 1.2 1.3 0.6 Using the above information, please determine the following a. b. c. Find the linear equation of regression of absences on salary for the line of best fit Compute the correlation coefficient (r) Please estimate the average number of absence for an employee earning $29,000

Explanation / Answer

SOlution:

code in R:

absences <- c(2.3,2,2,1.8,2.2,1.5,1.2,1.3,0.6)
salinthousands <- c(20,22.5,25,27.5,30,32.5,35,37.5,40)
mod1 <- lm(absences~salinthousands)
summary(mod1)

Output

Call:

lm(formula = absences ~ salinthousands)

Residuals:

Min 1Q Median 3Q Max

-0.33556 -0.09556 -0.03556 0.02444 0.54444

Coefficients:

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

(Intercept) 3.81556 0.42276 9.025 4.19e-05 ***

salinthousands -0.07200 0.01378 -5.226 0.00122 **

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

Residual standard error: 0.2668 on 7 degrees of freedom

Multiple R-squared: 0.796, Adjusted R-squared: 0.7669

F-statistic: 27.31 on 1 and 7 DF, p-value: 0.001218

regreesion eq from output is

number of absences=3.81556-0.07200 (salary)

slope=-0.07200

y intercept=3.81556

Solutionb:

r= -0.8921863

there exists a string negative relationship between

absences and salary

as no of absences increases ,salary decreases and vice versa

Solutionc:

substtitute X=29 in the regression eq obtained

number of absences=3.81556-0.07200 (salary)

number of absences=3.81556-0.07200 (29)

=1.727

=1.73

no of absences=1.73

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