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MGEC11 Week 3 Codes
Yue Yu
Fall 2023
library
(wooldridge)
Determinants of College GPA
data
(
gpa1
)
ols1
<-
lm
(colGPA
~
hsGPA
+
ACT,
data =
gpa1)
summary
(ols1)
##
## Call:
## lm(formula = colGPA ~ hsGPA + ACT, data = gpa1)
##
## Residuals:
##
Min
1Q
Median
3Q
Max
## -0.85442 -0.24666 -0.02614
0.28127
0.85357
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.286328
0.340822
3.774 0.000238 ***
## hsGPA
0.453456
0.095813
4.733 5.42e-06 ***
## ACT
0.009426
0.010777
0.875 0.383297
## ---
## Signif. codes:
0
***
0.001
**
0.01
*
0.05
.
0.1
1
##
## Residual standard error: 0.3403 on 138 degrees of freedom
## Multiple R-squared:
0.1764, Adjusted R-squared:
0.1645
## F-statistic: 14.78 on 2 and 138 DF,
p-value: 1.526e-06
Q1: What’s the impact of high school GPA on college GPA?
Holding all the other factors constant, an increase in high school GPA by one point leads to an increase in
college GPA by 0.45.
Q2: Is 0.45 a dramatic increase?
Compare the effect with the difference between 25 percentile and 75 percentile:
summary
(gpa1
$
colGPA)
##
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
##
2.200
2.800
3.000
3.057
3.300
4.000
College GPA at 75 percentile is 3.3 and college GPA at 25 percentile is 2.8. A 0.45 point increase in college
GPA moves one from 25 percentile to (almost) 75 percentile.
1
Q3: What’s the impact of ACT on college GPA?
Holding all the other factors constant, an increase in ACT by one point raises college GPA by only 0.01 point.
Compared to 0.5 or 0.37, this is a relatively small effect.
Q4: How much of the variation in college GPA can be explained by ACT and high school GPA?
Joint together, these two factors can explain 17.6% of the total variation in college GPA.
Q5: How to interpret the intercept?
The intercept 1.29 is the predicted college GPA if high school GPA and ACT are both set at zero. Since
no one who attends college has either a zero high school GPA or a zero on the ACT, the intercept in this
equation is not very meaningful.
2
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