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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.