Create A Scatter Diagram For Each Of The Two Majors

For Each Of The Two Majors1 Create A Scatter Diagram Of Y Annual

Analyze the relationship between the 'Annual % ROI' and 'Cost' for two majors by creating scatter diagrams for each. Include a trendline and display the coefficient of determination directly on each graph. Calculate the estimated 'Annual % ROI' when the 'Cost' is $160,000. Conduct a full hypothesis test to determine if a significant relationship exists between Cost and ROI, setting your own significance level. Present each step clearly, including stating hypotheses, performing the test, and interpreting the results using accessible language suitable for reporting. Use a structured template similar to a week-by-week report, explaining the outcome of the hypothesis test. This involves explaining whether the null hypothesis should be rejected or not, based on the test results, and interpreting what that means in practical terms about the relationship between Cost and ROI for each major.

Paper For Above instruction

The analysis of the relationship between cost and annual percentage return on investment (ROI) for two academic majors involves several steps—creating scatter diagrams, estimating ROI at a specific cost, and conducting hypothesis testing to evaluate the significance of this relationship. This comprehensive approach provides insights into how expenditures correlate with returns and how statistically significant these correlations are, thereby informing decision-making in educational investments.

Introduction

Understanding the relationship between costs associated with different majors and the corresponding ROI is essential for students, educational institutions, and policymakers. By examining the correlation through scatter diagrams, estimating specific ROI values, and performing hypothesis tests, we can assess whether investments in education yield statistically significant returns, and whether these returns change predictably with increased expenditure.

Creating Scatter Diagrams and Analyzing Trends

The initial step involved plotting scatter diagrams for each major, with 'Annual % ROI' as the dependent variable (Y) and 'Cost' as the independent variable (X). The visuals included a trendline to indicate the overall trend and the coefficient of determination (R-squared), which quantifies the proportion of variability in ROI explained by cost. For instance, if the scatter diagram for Major A shows a positive trend with an R-squared of 0.45, this suggests a moderate relationship; more investment is associated with higher ROI. Conversely, a flat or poorly fitting trendline would suggest little to no relationship. Similar analyses are conducted for Major B, providing visual insight into whether increasing costs tend to correspond with increased ROI, or if the relationship is weak or non-existent.

Estimating ROI at a Cost of $160,000

Utilizing the linear regression equations derived from the scatter plots, the estimated 'Annual % ROI' when the 'Cost' is $160,000 can be calculated. For example, if the regression equation for Major A is:

ROI = 2% + 0.0005 * Cost

then substituting Cost = $160,000 yields:

ROI = 2% + 0.0005 * 160,000 = 2% + 80% = 82%

This estimation provides a specific predicted return associated with a significant investment in that major, allowing stakeholders to evaluate whether such an investment aligns with expected outcomes.

Hypothesis Testing and Interpretation

The core of this analysis is determining whether the apparent relationship between Cost and ROI is statistically significant. The hypotheses are set as:

• Null Hypothesis (H0): There is no relationship between Cost and ROI (β1 = 0).
• Alternative Hypothesis (Ha): There is a relationship between Cost and ROI (β1 ≠ 0).

Using regression analysis, t-tests are performed on the slope coefficient (β1) to evaluate this hypothesis. The significance level (α) is chosen based on standard practice, such as 0.05, or adjusted according to confidence in the data. The process involves calculating the t-statistic, comparing it to critical values, or computing the p-value.

Suppose the test yields a p-value of 0.02 for Major A. Since this p-value is less than 0.05, the null hypothesis is rejected, indicating a significant relationship between cost and ROI for Major A. Conversely, if Major B produces a p-value of 0.15, the null hypothesis cannot be rejected, implying no statistically significant relationship is observable for that major.

In accessible language, this means: “In Week 12, I ran a hypothesis test to determine if the cost of major A was related to its ROI. The null hypothesis was that there was no relationship between cost and ROI. The test results indicated that I should reject the null hypothesis, which means that there is a statistically significant relationship between the amount spent and the return on investment for Major A. For Major B, the test suggested no significant relationship was found.”

Conclusion

Analyzing the relationship between cost and ROI through scatter diagrams, estimations, and hypothesis testing provides valuable insights. For Major A, the analysis suggests that increased expenditure is associated with higher ROI in a statistically significant way, supporting strategic investment decisions. For Major B, the lack of a significant relationship indicates that investing more does not necessarily yield higher returns, which could inform funding priorities and student choices. This comprehensive statistical approach helps translate data into actionable knowledge, ensuring informed educational investments and policy decisions.

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