In: Statistics and Probability
Individual | Bettendorf | Experience (X1) | Education (X2) | Sex (X3) |
1 | 53600 | 5.5 | 4 | F |
2 | 52500 | 9 | 4 | M |
3 | 58900 | 4 | 5 | F |
4 | 59000 | 8 | 4 | M |
5 | 57500 | 9.5 | 5 | M |
6 | 55500 | 3 | 4 | F |
7 | 56000 | 7 | 3 | F |
8 | 52700 | 1.5 | 4.5 | F |
9 | 65000 | 8.5 | 5 | M |
10 | 60000 | 7.5 | 6 | F |
11 | 56000 | 9.5 | 2 | M |
12 | 54900 | 6 | 2 | F |
13 | 55000 | 2.5 | 4 | M |
14 | 60500 | 1.5 | 4.5 | M |
1. What is the coefficient of determination between the three
predictors taken as a group and annual salary.
Select one:
a..323
b..772
c..522
d..771
2. Let X1 = experience, X2 = Education, and X3 = Sex, what is the multiple regression equation?
Select one:
a.Y= 2809 + 228.5(X1) + 560.6(X2) + 1287.4(X3)
b.Y=41462.6 + 337.3(X1) + 2169.3(X2) + 3097.0(X3)
c.Y=48951.9 + 195.3(X1) + 1480.6(X2) + 1595.1(X3)
d.Y= 42410.2 + 403.5(X1) + 1856.4(X2) + 2964.4(X3)
The R output of the given regresssion problem is given below.
Bettendorf<-c(53600,52500,58900,59000,57500,55500,56000,52700,65000,60000,56000,54900,55000,60500)
Experience<-c(5.5,9,4,8,9.5,3,7,1.5,8.5,7.5,9.5,6,2.5,1.5)
Education<-c(4,4,5,4,5,4,3,4.5,5,6,2,2,4,4.5)
Sex<-c(1,2,1,2,2,1,1,1,2,1,2,1,2,2)
model <- lm(Bettendorf~ Experience + Education +Sex)# Coding 1 for F and 2 for M
summary(model)
[1]
Call:
lm(formula = Bettendorf ~ Experience + Education + Sex)
Residuals:
Min 1Q Median 3Q Max
-5727.4 -2218.7 667.8 1632.5 5389.6
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 47356.8 4491.8 10.543 9.77e-07 ***
Experience 195.3 329.7 0.593 0.5667
Education 1480.6 809.0 1.830 0.0971 .
Sex 1595.1 1857.6 0.859 0.4106
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3249 on 10 degrees of freedom
Multiple R-squared: 0.3234, Adjusted R-squared: 0.1204
F-statistic: 1.593 on 3 and 10 DF, p-value: 0.2521
(1) From this R code We get coefficient of determination (Multiple ) as 0.32340.323. Therefore the corerct option is (a)0.323 .
(2) From the coefficients we get the estimates of the coefficients as follows,
Variables | Estimates |
Intercept | 47356.8 |
Experience(X1) | 195.3 |
Education(X2) | 1480.6 |
Sex(X3) | 1595.1 |
Therefore the equation of the regression line is . Hence the correct option is (c).
(In the given answer they wrongly given the intercept as 48951.9.)