ECON7020X Extra Credit [5 Points] Due October 26, 2020, 11:5 ✓ Solved
ECON7020X Extra credit [5 points] Due October 26, 2020, 11:59 PM Using the uploaded Excel file and any statistical software of your choosing, answer the following questions. The file gives data on average public teacher pay (annual salary in dollars) and spending on public schools per pupil (dollars) in 1985 for 50 states and the District of Columbia.
Using the uploaded Excel file and any statistical software of your choosing, answer the following questions. The file provides data on average public teacher pay (annual salary in dollars) and spending on public schools per pupil (dollars) in 1985 for 50 states and the District of Columbia.
1. Generate the regression output for the regression: [1]
2. Interpret the estimated slope coefficient.
3. Establish a 95% confidence interval for \(\beta\) (the slope coefficient). Will you reject the null hypothesis that the true slope coefficient is 3?
4. Conduct a hypothesis test that the slope of the variable Spend is zero using \(\alpha=0.01\). You must write out:
- a) the null and alternative hypothesis,
- b) the conclusion you’ve arrived at.
Sample Paper For Above instruction
The following analysis investigates the relationship between public school spending per pupil and average teacher salaries across the United States in 1985. Using regression analysis, the aim is to understand how changes in spending influence teacher salaries and to test specific hypotheses regarding this relationship.
The regression analysis begins with generating the regression output based on the provided dataset, which includes variables for teacher salaries and per-pupil school spending across 50 states and D.C. (Cameron & Trivedi, 2010). The regression equation models teacher salaries as a function of school spending, providing coefficients that quantify this relationship.
The estimated slope coefficient represents the average change in teacher pay associated with a one-dollar increase in school spending per pupil. A positive coefficient suggests that higher spending correlates with higher teacher salaries, whereas a negative coefficient indicates the opposite (Stock & Watson, 2015). Interpreting this coefficient involves examining its magnitude and statistical significance to assess practical and economic implications.
A 95% confidence interval for the slope coefficient is constructed to determine the precision of this estimate. If the interval contains the null hypothesis value of 3, we fail to reject the null; otherwise, we reject it (Wooldridge, 2013). This statistical interval helps us understand the plausible range of the true population parameter based on sample data.
Hypothesis testing is conducted to evaluate whether the slope coefficient differs significantly from zero, indicating a causal or associative effect of spending on salaries. Using an alpha level of 0.01, the null hypothesis (H0: \(\beta = 0\)) is tested against the alternative hypothesis (H1: \(\beta \neq 0\)). Based on the test statistic and p-value obtained from the regression output, a conclusion is drawn regarding the significance of school spending as a predictor of teacher salaries (Greene, 2012).
This analysis provides insight into the financial relationship within the educational system, informing policymakers and stakeholders on resource allocation and funding effectiveness. The results' statistical significance and confidence intervals guide decision-making and future research directions.
References
- Cameron, A. C., & Trivedi, P. K. (2010). Microeconometrics Using Stata. Stata Press.
- Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson Education.
- Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics (3rd ed.). Pearson.
- Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach. Cengage Learning.