Econometrics Essay Example
Interpretation of the OLS estimates
The OLS estimates are birth weight, average cigarettes smoked and family income. Birth weight is dependent on family income and the average cigarettes smoked during pregnancy. Birth weight is positively related to family income while negatively related to the average cigarettes smoked during pregnancy.
Holding fixed the amount of family income, an effect of 0.46 average cigarettes smoked reduces birth weight by 0.46. While an extra rise in family income with average cigarettes held constant, increases birth weight by 0.09.
The intercept of the model is 116.97, suggesting that if cigarette smoking and family income have no impact on infants’ birth weight; the weight of infants would average 116.97 ounces.
Smoking has an estimated coefficient of -0.46, with the estimate having a standard error of 0.09. Comparing regression estimates with the standard error enables an assessment of their statistical significance (Sen and Strivasava, p.179); if an estimated regression coefficient exceeds the standard error in its estimation, its influence on the outcome (dependent) variable has statistical significance. The ratio of the estimated coefficient of smoking to the standard error of the estimate is:
With a ratio of -5.111, the estimated coefficient of smoking is substantively lower than the standard error, implying that smoking does not have a statistically significant effect on infant health.
Ceteris paribus effect on birth weight increasing family income by $10, 0000
A dollar increase in family income- holding the other regression parameters constant- increases birth weight by 0.09 times. Thus, a $10,000 increase in family income will increase an infant’s birth weight by 10,000*0.09 = 900 ounces.
R2 of the regression and overall significance of the model
The R2 of the regression model stands at 0.0298, suggesting that the regression model explains approximately 2.98% of the variation in the infants’ birth weight. Testing the overall significance of the model requires the computation of the F-test statistic. The R Square can be expressed as (Chatterjee and Simonoff, p.105):
R Square = SSR/SST = 1 – (SSE/SSR) (SSR- regression sum of squares, SSE- error sum of squares, SST- total sum of squares).
With an R Square of 0.0298, the expression becomes:
2.98/100, with 2.98 representing the SSR, and 100 the SST.
The SSE, therefore, stands at:
SST – SSR = 100-2.98= 97.02
With the SSR and SSE, we can obtain the F test statistic using the formula (Hanneman, Kposowa, and Riddle, p. 216):
(SSR/k)/ ((SSE)/ (n—k-1)) (k is the number of independent variables, and n the number of cases)
Applying the formula to the problem:
= (2.98/2)/ (97.02/1385)
The critical value of the F-distribution at a 0.05 significance level, 2 degrees of freedom in the numerator at 1385 degrees of freedom in the denominator, is 3.8415. Considering that the computed F-statistic exceeds the critical value of the F distribution, the regression model is significant.
At the significant levels: 0.05 and 0.01, the computed F-statistic is non-significant, indicating that the overall model is not significant.
i) appropriateness of transforming faminc into natural logarithm:
Transforming this variable helps in ensuring that the distribution of the data is approximately normal, as well as in reducing the variance of the faminc data. Regression analysis yields valid results when data is homogenous and normally distributed; thus, transforming the faminc variable will enhance the accuracy of the estimated regression parameters.
ii) Ceteris paribus, effect of a 10% increase in income:
A percentage increase in family income leads to an increase in birth weight by a multiple of 1.85: a 10% income increase will increase birth weight by 1.85*10 = 18.5 ounces.
i) Improvement of the model following the inclusion of additional variables:
Model 2 has an R Square of 0.0295; for model 3, the R-square is 0.0520.
The F-test statistic for model 2:
The F-test statistic for model 3:
The inclusion of additional variables has improved the model; with additional variables, the model can explain a larger proportion of variation in the dependent variables, with the F test statistics showing that the model is still significant.
ii) Coefficients of male and white:
Monitoring for the influence of other variables in the regression model, the weight of male infants is 3.151 times that of infants belonging to other gender categories, and ceteris paribus, the weight of white infants is 5.666 times that of infants belonging to other races.
iii) Impact of the inclusion of other variables
The inclusion of additional variables has reduced the effect of income because other variables probably moderate the relationship between family income and an infant’s weight at birth. For instance, family income has a stronger impact on infant weight when the mother has few years of education than it does when the mother has more years of education.
Summary of the findings:
Smoking has an adverse effect on infant health because, for every cigarette smoked by an expectant woman, the weight of an infant at birth approximately falls by a multiple of 0.46. Although the coefficient of smoking is not statistically significant, the regression model is significant, overall; this means that smoking being one of the coefficients of the significant regression models- affects infant health. In addition, smoking interacts with other factors such as family income, race and an infant’s gender in its influence on infant health.
Chatterjee, Samprit, and Jeffrey S. Simonoff. Handbook of regression analysis. Vol. 5. John Wiley & Sons, 2013.
Hanneman, Robert A., Augustine J. Kposowa, and Mark D. Riddle. Basic statistics for social research. Vol. 38. John Wiley & Sons, 2012.
Sen, Ashish, and Muni Srivastava. Regression analysis: theory, methods, and applications. Springer Science & Business Media, 2012.
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