TABLE 12-2 A professor of industrial relations believes that an individual\'s wa
ID: 3151995 • Letter: T
Question
TABLE 12-2
A professor of industrial relations believes that an individual's wage rate
at a factory (Y) depends on his performance rating (X1) and the number of
economics courses the employee successfully completed in college (X2). The
professor randomly selects 6 workers and collects the following information:
Employee Y ($) X1 X2
ÄÄÄÄÄÄÄÄ ÄÄÄÄÄ ÄÄ ÄÄ
1 10 3 0
2 12 1 5
3 15 8 1
4 17 5 8
5 20 7 12
6 25 10 9
Referring to Table 12-2, suppose an employee had never taken an
economics course and managed to score a 5 on his performance rating.
What is his estimated expected wage rate?
a. 10.90
b. 12.20
c. 17.23
d. 25.11
Explanation / Answer
As mention in the above question, individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2).
y: 10,12,15,17,20,25
x1: 3,1,8,5,7,10
x2: 0,5,1,8,12,9
To fit the regression model we use the R- Software and code is mention here
> y<-c(10,12,15,17,20,25)
> x1<-c(3,1,8,5,7,10)
> x2<-c(0,5,1,8,12,9)
> fit<-lm(y~x1+x2) # fit the linear multiple regression model
> fit
Call:
lm(formula = y ~ x1 + x2)
Coefficients:
(Intercept) x1 x2
6.932 1.054 0.616
On the basis of the given sample regression model can we written as
Y = 6.932 + 1.054 * X1 + 0.616 * X2
> summary(fit)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
1 2 3 4 5 6
-0.09496 0.93366 -0.98274 -0.13180 -1.70458 1.98042
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.9319 1.5549 4.458 0.0210 *
x1 1.0544 0.2459 4.288 0.0233 *
x2 0.6160 0.1737 3.546 0.0382 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.702 on 3 degrees of freedom
Multiple R-squared: 0.9419, Adjusted R-squared: 0.9031
F-statistic: 24.3 on 2 and 3 DF, p-value: 0.01402
> fit$fitted.value # To calculate the estimated wage rate at a factory
1 2 3 4 5 6
10.09496 11.06634 15.98274 17.13180 21.70458 23.01958
> mean(fit$fitted.value) # to calculate the estimated expected wage rate
[1] 16.5
henece after finding the coefficent we find the estimates wage rate and then take mean that estimated value is 16.5.
ANS : (c)
Note : approximatel this option is nearest options among the given option.
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