MAT 303 Module Three Problem Set Report Template

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Southern New Hampshire University *

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Mathematics

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Apr 3, 2024

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MAT 303 Module Three Problem Set Report Second Order Models Diego Beteta diego.beteta@snhu.edu Southern New Hampshire University

Note: Replace the bracketed text on page one (the cover page) with your personal information. 1. Introduction The economic dataset includes variables such as wage growth, inflation, unemployment, economic conditions (recession or no recession), levels of education, and GDP. This data is likely a historical record intended to study how different economic factors are associated with wage growth in the labor force. Our results could be vital for policymakers and economists to understand the dynamics of wage growth, helping to inform decisions and create strategies for economic development. The analyses will likely involve statistical methods to determine correlations, trends, and potentially predictive modeling to estimate future wage growth under different economic scenarios. We might employ regression analysis to understand the relationships between wage growth and other factors and time-series analysis if the data is chronological to look at the trends over time. 2. Data Preparation The important variables in this dataset that we're focusing on include:  Wage Growth : This measures the percentage increase in labor force wages. Understanding this helps to evaluate workers' standard of living and economic prosperity.  Inflation : Inflation represents the rate at which the general level of prices for goods and services rises and, subsequently, how purchasing power is falling. Analyzing inflation alongside wage growth can indicate whether wage increases keep pace with the cost of living.  GDP (Gross Domestic Product) Growth : GDP growth is the increase in the production and consumption of goods and services in an economy. It's a broad measure of overall economic activity and health. These variables are crucial as they interplay to define a country's or region's economic condition, influencing policy decisions. Regarding the structure of the dataset, it consists of 99 rows and 6 columns. Each row represents an entry (potentially a year or other time frame). In contrast, the columns represent the variables mentioned, including wage growth, inflation, GDP growth, and other related economic factors. 3. Quadratic (Second Order) Model with One Quantitative Variable Correlation Analysis 2

Our scatterplot shows how wage growth compares with the unemployment rate. The relationship between the two isn't a straight line, indicating that the connection isn't just a simple increase or decrease. The pattern suggests that as unemployment changes, the effect on wage growth might increase initially and then decrease, or the opposite, forming more of a curve than a straight line. The scatterplot shows that the relationship between wage growth and unemployment is not perfectly linear. The data points do not align in a straight line, which suggests that a first order (linear) model might not be the best fit. Instead, the data points show a pattern that could be a curve, hinting that unemployment's impact on wage growth isn't constant as unemployment changes. Given this observation, a second order (quadratic) model might be more appropriate, which would allow for a curve that can bend upwards or downwards. This model can account for a more complex relationship where the effect of unemployment on wage growth could increase or decrease at different unemployment rates rather than changing at a constant rate, as a linear model would suggest. Reporting Results Report the results of the regression model. Address the following questions in your analysis:  General Form: y = β 0 + β 1 x + β 2 x 2  Prediction Equation: ^ y = ^ β 0 + ^ β 1 unemployment + ^ β 2 unemployment 2  Second-order regression model for wage growth using unemployment as the independent variable: ^ wage growth = 12.2342 − 1.7432 unemployment + 0.0674 unemployment 2 3

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