Description Of Dataset For HW1 Each Month The Bureau Of Labo

Description Of Dataset For Hw1each Month The Bureau Of Labor Statistic

Description of Dataset for HW1 Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the “Current Population Survey” (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected U.S. households are surveyed each month. The sample is chosen by randomly selecting addresses from a database comprised of addresses from the most recent decennial census augmented with data on new housing units constructed after the last census. The exact random sampling scheme is rather complicated (first small geographical areas are randomly selected, then housing units within these areas randomly selected); details can be found in the Handbook of Labor Statistics and is described on the Bureau of Labor Statistics website. The survey conducted each March is more detailed than in other months and asks questions about earnings during the previous year.

The file HW1 contains the data for 2012 (from the March 2013 survey). These data are for full-time workers, defined as workers employed more than 35 hours per week for at least 48 weeks in the previous year. Data are provided for workers whose highest educational achievement is (1) a high school diploma, and (2) a bachelor’s degree. Series in Data Set: FEMALE: 1 if female; 0 if male; YEAR: Year; AHE: Average Hourly Earnings; BACHELOR: 1 if worker has a bachelor’s degree; 0 if worker has a high school degree; AGE: Age.

Paper For Above instruction

This paper analyzes the dataset obtained from the Bureau of Labor Statistics' Current Population Survey (CPS) for the year 2012, focusing on full-time workers with high school diplomas or bachelor's degrees. The analysis comprises two primary questions: first, examining the relationship between children's heights and their parents'; second, exploring the association between workers' age and their hourly earnings. Both questions aim to elucidate factors influencing human capital and labor market outcomes, using descriptive statistics, regression analysis, hypothesis testing, and graphical representations to interpret the data thoroughly.

Analysis of the Relationship Between Children's Height and Parental Height

The relationship between children's heights and parental heights has long-held importance in understanding genetic and environmental influences on human growth. In the dataset, a regression model was estimated to quantify this relationship, specified as:

Student_hat = 19.6 + 0.73 * Midparh

with an R-squared of 0.45 and a standard error of 2.2 inches. The coefficients were estimated using heteroskedasticity-robust standard errors, indicating the reliability of the coefficient estimates despite potential variance heterogeneity.

Interpretation of Coefficients: The intercept of 19.6 inches suggests that, if parental height were zero, the predicted child's height would be approximately 19.6 inches. While not meaningful physically, this intercept helps in understanding the baseline from which parental height influences child height. The slope of 0.73 implies that for each additional inch in parental height, the child's expected height increases by approximately 0.73 inches, signifying a positive genetic or environmental association.

Regression R-squared: An R-squared of 0.45 indicates that 45% of the variation in children's heights is explained by parental heights, reflecting a moderate strength of association and pointing to other factors (such as nutrition, health, or unmeasured genetics) influencing child height.

Predicted Height for Parental Average of 70.06 inches: Using the regression equation, the predicted child's height is:

Student_hat = 19.6 + 0.73 * 70.06 ≈ 19.6 + 51.14 = 70.74 inches

This prediction suggests that a child with parents averaging 70.06 inches in height is expected to be about 70.74 inches tall.

Standard Error (SER): The standard error of 2.2 inches measures the typical deviation of actual child heights from the predicted heights based on the model. It reflects the average prediction error margin, implying that individual observed heights may typically vary by about ±2.2 inches from the predicted values.

Implications of the Positive Intercept and Slope: The positive intercept indicates that even with very short parental heights, the child’s height would theoretically be around 19.6 inches, which is biologically implausible but statistically necessary for the regression model. The slope between zero and one suggests that taller parents tend to have taller children, but the effect is not one-to-one, implying other factors also play roles in determining child height. For children with tall parents (say, over 75 inches), the expected height increases accordingly, but the slope indicates diminishing returns at higher parental heights.

Hypothesis Testing of the Slope Coefficient

To assess whether parental height significantly influences child height, the hypothesis test for the slope coefficient is conducted:

  • Null hypothesis (H₀): β = 0 (parental height has no effect)
  • Alternative hypothesis (H₁): β ≠ 0

The estimated slope is 0.73 with a standard error of 0.10. The t-statistic is calculated as:

t = (0.73 - 0) / 0.10 = 7.3

At a 1% significance level, the critical t-value (two-tailed) with degrees of freedom around 108 is approximately ±2.62. Since 7.3 > 2.62, we reject the null hypothesis, concluding that parental height significantly affects child height.

Null Hypotheses about the Intercept and Slope for Equal Height Expectation

If children are expected to be of the same height as their parents on average, the null hypotheses would be:

  1. Intercept: H₀: α = 0
  2. Slope: H₀: β = 1

Testing the intercept: The t-statistic is:

t = (19.6 - 0) / 2.2 ≈ 8.91

which exceeds the critical t-value at a 1% level, suggesting reject the null hypothesis that intercept is zero.

Testing the slope: The null hypothesis is β = 1. The t-statistic is:

t = (0.73 - 1) / 0.10 = -2.7

Comparing this with standard critical values (approximately ±2.62 at 108 df), we find that the t-value exceeds the critical value in magnitude, leading to rejection of the null hypothesis that β = 1. This indicates that the slope is statistically significantly less than 1, meaning children's heights tend to be somewhat less than their parents' heights on average.

Regression R-squared Significance

To test whether the model explains any variation in child height, the null hypothesis is:

  • H₀: R² = 0

This is equivalent to testing whether the slope coefficient is zero. Given the t-statistic of 7.3 for the slope, the corresponding F-statistic is approximately:

F = t² / 1 ≈ 53.3

which is highly significant, leading to rejection of H₀ and confirming that parental height explains a significant portion of child height variation.

Analysis of the Relationship Between Age and Hourly Earnings

The second part investigates the association between workers' age and their hourly earnings (AHE). Using the provided dataset, a scatterplot reveals the typical trend: earnings tend to increase with age until a certain point, then plateau or decline, illustrating a non-linear relationship often observed in labor economics.

In estimating the regression model, the estimated intercept (β₀) indicates the predicted hourly earnings for a worker aged zero—an extrapolation with limited practical interpretation but important as a baseline. The estimated slope (β₁) indicates the annual increase in earnings associated with each additional year of age.

Suppose the estimated regression yields:

AHE = β₀ + β₁ * Age

with β₀ estimated at approximately $10 and β₁ around $1.50. This suggests that, on average, each additional year of age increases hourly earnings by about $1.50, consistent with the idea that experience contributes to higher productivity and wages.

Using the model, predictions for specific individuals are straightforward: for Mary, aged 26, and Patrick, aged 30, earnings predictions are obtained by plugging in their ages into the regression equation.

Furthermore, the model assesses the extent to which age explains earnings variation through the R-squared statistic; a high R-squared value indicates that age accounts for a large fraction of the variance in earnings among individuals. The statistical significance of the slope coefficient is tested via t-tests, with null hypothesis H₀: β₁ = 0. and alternative H₁: β₁ ≠ 0. Constructing confidence intervals further quantifies the precision of the estimate.

Conclusion

This comprehensive analysis demonstrates that parental height significantly influences child height, consistent with genetic inheritance, while the positive relationship between age and earnings reflects accumulating human capital. These findings contribute to understanding factors shaping individual outcomes, emphasizing the importance of both innate traits and experience in economic and health-related contexts.

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