Economics 113uc Santa Cruz Summer 2020 Assignment 21 The Fol

Economics 113uc Santa Cruzsummer I 2020assignment 21 The Following

Analyze the relationship between minimum wage and unemployment rates across multiple states by creating graphical and statistical models. Graph unemployment rates against minimum wages, fit a line, and interpret its characteristics. Calculate variance and covariance to understand data variability and relationships. Estimate a regression of unemployment on minimum wage, interpret the coefficients, and compare with the graph. Use the estimated model to predict unemployment rates for specific minimum wages, analyze changes, and compute prediction errors and R-squared for the model. Examine the assumptions necessary for regression through the origin and compare results with the standard regression. Apply similar analyses to wages and shirts produced in a factory, and interpret regression coefficients and predictions. Additionally, analyze data on days sick versus age, including binary sick status and age groups, interpreting model coefficients and calculating prediction errors. Study stock prices in relation to profits per share and litigation, interpreting coefficients, making predictions, and understanding the effect of lawsuits. Examine relationships between exercise hours and weight, with regressions on both hours and log-hours, interpreting coefficients and predicting changes. Use a dataset on students' GPA, high school GPA, skipped lectures, and ACT scores to estimate predictive models, interpret coefficients, and compare models for different student groups. Explore the relationships between GPA, high school GPA, and ACT scores both in raw and logged scales, predicting values and assessing the predictive power of these variables.

Paper For Above instruction

Analyzing the relationship between minimum wage and unemployment across states provides critical insights into labor market dynamics. The initial step involves plotting the unemployment rates against the minimum wages for six states, fitting a best-line, and interpreting its slope and intercept. The graph facilitates visualization of the correlation, while the line's slope indicates the rate at which unemployment changes with shifts in the minimum wage. A positive slope would suggest that higher minimum wages are associated with higher unemployment, aligning with classical economic hypotheses, whereas a negative slope could imply differing dynamics or other influencing factors.

Using statistical measures, the variances of unemployment and minimum wage are calculated to assess their respective variability. Covariance measures how these two variables change together. A positive covariance indicates that both variables tend to increase or decrease simultaneously, whereas a negative covariance suggests inverse movement. These calculations set the foundation for the regression analysis, where unemployment rate is modeled as a function of minimum wage through Ordinary Least Squares (OLS) estimation.

The estimated regression equation typically takes the form: Unemployment = α + β × Minimum Wage + ε. Here, β represents the change in unemployment rate associated with a one-dollar increase in minimum wage. Interpreting this coefficient involves framing it within the context—if β is positive, for instance, then increasing the minimum wage by one dollar predicts a certain increase in unemployment proportionally. Comparing this estimated slope to the approximations derived from the graph helps verify the consistency between the visual and statistical analyses.

Next, employing the regression equation to make predictions involves plugging in specific minimum wage values. For example, with a minimum wage of $10, the predicted unemployment rate is computed from the estimated model. This prediction can then be contrasted with the actual unemployment rate in California to evaluate accuracy. If the real figure deviates significantly, it may suggest other factors influencing unemployment in California beyond minimum wage variations.

Further, the model can be used to analyze how an increase in minimum wage from $10 to $15 affects unemployment. The predicted change is obtained by multiplying the change in wage by the estimated coefficient β. Assessing the magnitude and significance of this change provides insights into policy implications.

Prediction errors for each state are computed by comparing actual unemployment rates with those predicted by the regression model, highlighting the individual discrepancies. Calculating R-squared quantifies the model's explanatory power, reflecting the proportion of variation in unemployment explained by minimum wage. An R-squared close to 1 indicates a well-fitting model, whereas lower values suggest more factors influence unemployment.

Regarding regression through the origin, this approach assumes that when minimum wage is zero, unemployment is also zero, an assumption that often lacks economic realism given background unemployment. Nonetheless, we can estimate such a model by setting the intercept to zero and recalculating coefficients. Such models can sometimes simplify analysis but may lead to biased or inconsistent estimates if the assumption doesn't hold.

The analysis extends to other contexts, such as wages and shirts produced, where similar assumptions about linear relationships through the origin are examined. Regression coefficients from these models are interpreted to quantify the impact of shirts made on wages, predicting wages for specific shirt quantities, and understanding how production scales affect earnings.

Additional analyses involve studying how the number of sick days correlates with age, using both standard regression and binary outcome models. The coefficient on age indicates how days sick change with age—specifically, each additional year increases sick days by an estimated amount. In predicting sick days for specific ages and calculating prediction errors, the model's accuracy is assessed. The binary sick status variables allow interpretation of the likelihood of being sick given age-related indicators, such as being classified as a senior.

Similarly, regressions involving stock price as affected by profits per share and lawsuits quantify how legal challenges and profitability influence stock valuations. The detail of coefficient interpretation clarifies how lawsuits negatively impact stock prices, and predictions are made for specific profit levels and lawsuit counts. The analysis also examines how profits need to change to offset lawsuit effects, providing insights into company valuation dynamics.

The relationship between exercise hours and weight is modeled with regressions on both hours and their natural logarithm. Interpretation of coefficients reveals how physical activity influences weight directly or proportionally when considering log transformation. Predicted changes from moving between exercise levels exemplify how lifestyle changes can quantitatively affect health indicators.

Lastly, the analysis of college GPA data uses regressions on ACT scores and high school GPA, interpreting coefficients capable of predicting college success based on these standardized metrics. Model predictions for specific scores, along with the assessment of how well ACT scores explain GPA variation, inform understanding of standardized testing's predictive power. Comparing models for students with different lecture-avoidance behaviors evaluates whether certain groups lend themselves better to prediction, providing nuanced insights into factors influencing academic performance.

This comprehensive analysis demonstrates how regression models are powerful tools in economics and social sciences, enabling quantitative assessment of relationships among variables, predictions, and policy implications. Critical interpretation of coefficients, model fit, assumptions, and predictions provides robust insights essential for informed decision-making and further research.

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