Correlation Coefficient Questions

Correlation: Relating Two Variables

Classic economic theory states that as the price of something goes up, the demand for it goes down. For example, a new Ferrari can cost over $250,000. Not a lot of people can pay that price, and that is one reason why you do not see many people driving the new Ferraris. Classic economic theory also states that raising the minimum wage would increase unemployment because employers would not be able to pay the higher cost of wages. However, statistical analysis has shown that raising the minimum wage does not actually correlate with increased unemployment. Card and Krueger (1993) compared unemployment rates in New Jersey and Pennsylvania when New Jersey raised its minimum wage in 1992 from $4.25/hour to $5.05/hour and the minimum wage in Pennsylvania remained the same. These states are neighbors and shared enough traits in common to make the comparison appropriate. The researchers did not find that the increase in the minimum wage had any correlation with a negative impact on job growth. Using correlation to determine the relationship among two variables can be applied to many fields to explore how to effect positive social change.

Reference: Card, D., & Krueger, A. B. (1993). Minimum wages and employment: A case study of the fast food industry in New Jersey and Pennsylvania (No. w4509). Cambridge, MA: National Bureau of Economic Research.

For this Discussion, you will expand the political affiliation dataset you created in Week 7 (i.e., US Demographic Information PA).

To Prepare:

  • Based on the political affiliation dataset from Week 7, add an additional column (variable) to your dataset and name it “Population Size.” This variable will be the most current population of each state.
  • Search the Internet for a reliable source and locate the population size for each state. Input the most current population size for each state designated in your dataset.
  • Use your PSPP software, or a statistical software program of your choice, to help you correlate your data for this Discussion.
  • For students using the PSPP statistical software program, review the Learning Resources document Working With Datasets Job Aid for information about how to complete the tasks identified in the To Prepare and Post activities.

By Day 4,

Post the correlation coefficient between population size and income in the United States for one chosen year (i.e., Pearson Correlation). Report your source(s) of information for your dataset. Next, based on the p value (for Sig. 2-tailed) determine whether there is a statistically significant relationship between population size and income in the United States for the chosen year. Explain how big this correlation is and what this means. Next, create and post a scatterplot of your correlation and provide a brief explanation of your scatterplot.

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