Complete Problem 314 Of Chapter 3 And Submit To Your Instruc ✓ Solved

Complete Problem 314 Of Chapter 3 And Submit To Your Instructor Comp

Complete Problem 3.14 of Chapter 3. Table 3-6 gives data on X (net profits after tax in U.S. manufacturing industries [$, in millions]) and Y (cash dividend paid quarterly in manufacturing industries [$, in millions]) for years 1974 to 1986. What relationship, if any, do you expect between cash dividend and after-tax profits?

Plot the scattergram between Y and X. Does the scattergram support your expectations in part (a)? If so, do an OLS regression of Y on X and obtain the usual statistics. Establish a 99% confidence interval for the true slope and test the hypothesis that the true slope coefficient is zero; that is, there is no relationship between dividend and the after-tax profit.

Paper For Above Instructions

In the analysis of financial metrics such as net profits after tax and cash dividends in manufacturing industries, it is essential to explore the relationship between these two variables. The time frame under consideration spans from 1974 to 1986, and we will utilize data on net profits after tax (X) and cash dividends paid quarterly (Y) to understand their correlation.

Understanding the Variables

Net profits after tax (X) represent the financial success of manufacturing firms, indicating how much profit they retain after tax deductions. Cash dividends (Y), on the other hand, are a distribution of a portion of a company's earnings to its shareholders, reflecting how firms return value to their investors.

Expected Relationship

It is reasonable to expect a positive correlation between after-tax profits and cash dividends. As companies generate higher profits, they are more likely to distribute a significant portion of these earnings as dividends, which serves to attract and retain investors. Conversely, in times of lower profitability, firms may choose to conserve cash by reducing or omitting dividends.

Scattergram Analysis

To visualize the relationship between X and Y, a scattergram is constructed. Each point on the scattergram represents a pair of values (X, Y) corresponding to the profits and dividends in specific years from 1974 to 1986. If the scatterplot indicates a trend where increases in X correspond to increases in Y, this would support the hypothesis of a positive relationship.

OLS Regression

Ordinary Least Squares (OLS) regression is employed to quantify this relationship. The regression equation can be expressed as follows:

Y = β0 + β1 * X + ε

Where:

• Y is the dependent variable (cash dividends)
• X is the independent variable (net profits after tax)
• β0 is the y-intercept
• β1 is the slope coefficient
• ε is the error term

After performing the regression analysis, we obtain coefficients for β0 and β1 along with statistical measures such as R-squared value, which indicates the proportion of variance in Y explained by X. A significant β1 would confirm a relationship between profits and dividends.

99% Confidence Interval

To establish a 99% confidence interval for the true slope (β1), we can apply the formula:

CI = β1 ± (z * SE(β1))

Where:

• z is the z-value corresponding to the desired confidence level (for 99%, z ≈ 2.576)
• SE(β1) is the standard error of the slope estimate

This interval provides a range in which we expect the true slope to lie, giving us insight into the reliability of our estimate.

Hypothesis Testing

Next, we test the null hypothesis (H0: β1 = 0) against the alternative hypothesis (H1: β1 ≠ 0). This test assesses whether there is sufficient evidence to state that a relationship exists between after-tax profits and cash dividends. The test statistic can be calculated using the t-ratio:

t = (β1 - 0) / SE(β1)

We compare this t-value to the critical t-value from the t-distribution table at the desired level of significance (for a two-tailed test at 0.01) to draw our conclusions regarding the hypothesis.

Conclusion

In summary, analyzing the relationship between cash dividends and net profits will provide insights into corporate behavior concerning profit distribution. After preparing the scattergram, executing the OLS regression, calculating the confidence intervals, and conducting hypothesis tests, we can arrive at informed conclusions regarding whether or not net profits after tax significantly impact the cash dividends in U.S. manufacturing industries.

References

• Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach. South-Western Cengage Learning.
• Gujarati, D. N. & Porter, D. C. (2009). Basic Econometrics. McGraw-Hill Education.
• Studenmund, A. H. (2016). Using Econometrics: A Practical Guide. Pearson.
• Stock, J. H., & Watson, M. W. (2019). Introduction to Econometrics. Pearson.
• Brooks, C. (2014). Introductory Econometrics for Finance. Cambridge University Press.
• Hyndman, R. J., & Koehler, A. B. (2006). Another Look at Measures of Forecast Accuracy. FORESIGHT: The International Journal of Applied Forecasting, 4, 13-16.
• Freedman, D. A. (2009). Statistical Models: Theory and Practice. Cambridge University Press.
• Berenson, M. L., & Levine, D. M. (2018). Basic Business Statistics. Pearson.
• Keller, G. & Warrack, B. (2018). Statistics for Management and Economics. Cengage Learning.
• McClave, J. T., & Sincich, T. (2017). Statistics. Pearson.