A dataset contains data on birth weights of 65535 babies born in June 1997along with variables that are potentially related to birth weights. The sampleis restricted to singleton births, with mothers recorded as either black orwhite, between the ages of 18 and 45, resident in the United States.With the aim to investigate factors influencing the weight of babies atbirth, a regression of W eight on a range of variables has been carried out.A description of variables is given below and the estimation results can befound on the following page.Referring to these results, answer the following questions. Keep in mindthat two of the regressors, Mom_Age and M_W tGain, are entered in theregression in terms of the deviations from their mean. (a) Interpret the estimated intercept The last two variables are entered into the regression as centered around theirmean, Mom_Age_Cntrd and M_WtGain_Cntrd, i.e. Mom_Age_Cntrdis the variable Mom_Age minus the average age of Mom_Age, and simi-larly for M_WtGain_Cntrd. The average age of mothers is 27.2 years andthe average weight gain is 30.8 pounds.Dependent Variable: WEIGHTMethod: Least SquaresDate: 03/11/22 Time: 15:19Sample: 1 65535Included observations: 65535Huber-White-Hinkley (HC1) heteroskedasticity consistent standard errorsand covarianceVariableCoefficientStd. Errort-StatisticProb.3316.786104.65288.106849409.13380.0000BOY4.23195224.729210.0000MARRIED66.440965.69930611.657730.0000ED_COLED_HSED_SMCOLSMOKE27.517047.8160313.5205900.00048.6800206.4945971.3364980.181424.48548-200.6533-1.260510-200.52437.2292663.3869940.000711.36470-17.655850.0000CIGSPER0.812260-1.5518550.1207BLACK6.468994-30.997750.00005.6419210.46199612.212050.0000MOM_AGE_CNTRDMOM_AGE_CNTRD^2 -0.514637M_WTGAIN_CNTRDM_WTGAIN_CNTRD^2 -0.0279130.064432-7.9873460.00009.6189490.19833748.498020.00000.008685-3.2140420.00130.113853 Mean dependent var0.113691 S.D. dependent var541.4975 Akaike info criterionR-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statisticProb(F-statistic)Prob(Wald F-statistic)3347.636575.180015.426751.92E+10 Schwarz criterion15.42856-505483.1 Hannan-Quinn criter.15.42731701.5267 Durbin-Watson stat1.9571470.000000 Wald F-statistic623.64610.000000

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A dataset contains data on birth weights of 65535 babies born in June 1997
along with variables that are potentially related to birth weights. The sample
is restricted to singleton births, with mothers recorded as either black or
white, between the ages of 18 and 45, resident in the United States.
With the aim to investigate factors influencing the weight of babies at
birth, a regression of W eight on a range of variables has been carried out.
A description of variables is given below and the estimation results can be
found on the following page.
Referring to these results, answer the following questions. Keep in mind
that two of the regressors, Mom_Age and M_W tGain, are entered in the
regression in terms of the deviations from their mean.

(a) Interpret the estimated intercept

The last two variables are entered into the regression as centered around their
mean, Mom_Age_Cntrd and M_WtGain_Cntrd, i.e. Mom_Age_Cntrd
is the variable Mom_Age minus the average age of Mom_Age, and simi-
larly for M_WtGain_Cntrd. The average age of mothers is 27.2 years and
the average weight gain is 30.8 pounds.
Dependent Variable: WEIGHT
Method: Least Squares
Date: 03/11/22 Time: 15:19
Sample: 1 65535
Included observations: 65535
Huber-White-Hinkley (HC1) heteroskedasticity consistent standard errors
and covariance
Variable
Coefficient
Std. Error
t-Statistic
Prob.
3316.786
104.6528
8.106849
409.1338
0.0000
BOY
4.231952
24.72921
0.0000
MARRIED
66.44096
5.699306
11.65773
0.0000
ED_COL
ED_HS
ED_SMCOL
SMOKE
27.51704
7.816031
3.520590
0.0004
8.680020
6.494597
1.336498
0.1814
24.48548
-200.6533
-1.260510
-200.5243
7.229266
3.386994
0.0007
11.36470
-17.65585
0.0000
CIGSPER
0.812260
-1.551855
0.1207
BLACK
6.468994
-30.99775
0.0000
5.641921
0.461996
12.21205
0.0000
MOM_AGE_CNTRD
MOM_AGE_CNTRD^2 -0.514637
M_WTGAIN_CNTRD
M_WTGAIN_CNTRD^2 -0.027913
0.064432
-7.987346
0.0000
9.618949
0.198337
48.49802
0.0000
0.008685
-3.214042
0.0013
0.113853 Mean dependent var
0.113691 S.D. dependent var
541.4975 Akaike info criterion
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Prob(Wald F-statistic)
3347.636
575.1800
15.42675
1.92E+10 Schwarz criterion
15.42856
-505483.1 Hannan-Quinn criter.
15.42731
701.5267 Durbin-Watson stat
1.957147
0.000000 Wald F-statistic
623.6461
0.000000

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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