Regressor
Residual
Residual Sum of Squares
(SSR)
Response Variable
R
-squared
Sample Regression Function
(SRF)
Semi-elasticity
Simple Linear Regression
Model
Slope Parameter
Standard Error of
ˆ
1
Standard Error of the
Regression (SER)
Sum of Squared Residuals
(SSR)
Total Sum of Squares (SST)
Zero Conditional Mean
Assumption

62
Part 1
Regression Analysis with Cross-Sectional Data
(i)
Estimate the relationship between
GPA
and
ACT
using OLS; that is, obtain the
intercept and slope estimates in the equation
1
GPA
ˆ
0
ˆ
1
ACT
.
Comment on the direction of the relationship. Does the intercept have a useful inter-
pretation here? Explain. How much higher is the
GPA
predicted to be if the
ACT
score is increased by five points?
(ii)
Compute the fitted values and residuals for each observation, and verify that the
residuals (approximately) sum to zero.
(iii) What is the predicted value of
GPA
when
ACT
20?
(iv)
How much of the variation in
GPA
for these eight students is explained by
ACT
?
Explain.
2.4
The data set BWGHT.RAW contains data on births to women in the United States. Two
variables of interest are the dependent variable, infant birth weight in ounces (
bwght
),
and an explanatory variable, average number of cigarettes the mother smoked per day
during pregnancy (
cigs
). The following simple regression was estimated using data on
n
1,388 births:
1
bwght
119.77
0.514
cigs
(i) What is the predicted birth weight when cigs 0? What about when
(i) Interpret the intercept in this equation, and comment on its sign and magnitude.(ii) What is the predicted consumption when family income is $30,000?

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- Fall '14
- Econometrics, Regression Analysis, simple regression model