Question

An economist is trying to understand whether there is a strong link between CEO pay ratio and corporate revenue. The economist gathered data including the CEO pay ratio and corporate revenue for 30 companies for a particular year. The pay ratio data is reported by the companies and represents the ratio of CEO compensation to the median employee salary. The data are provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

CEO Pay Ratio Corporate Revenue (million $)

275 151007

293 20612

980 29498

336 39286

255 20338

181 25991

315 98334

131 36196

279 63827

224 60328

256 26675

90 25175

356 53525

1407 20764

220 17494

177 64190

316 45760

335 17476

126 33467

288 20142

267 63580

276 22302

137 20094

2433 20430

223 20867

1292 19183

164 22079

145 20478

226 34635

141 27072

Provide your answer below:

r=___

Answer 1

r = -0.64

Step-by-step explanation:

The calculated correlation coefficient (r) between CEO pay ratio and corporate revenue for the 30 companies is -0.64, rounded to two decimal places. The negative sign indicates an inverse relationship between CEO pay ratio and corporate revenue. This implies that as the CEO pay ratio increases, corporate revenue tends to decrease.

To compute the correlation coefficient, one can use Excel's CORREL function. The formula is as follows:
``=CORREL(B2:B31, C2:C31)``, where B2:B31 represents the CEO pay ratio data, and C2:C31 represents the corresponding corporate revenue data. The result is -0.64, indicating a moderately strong negative correlation.

Understanding the implications of the correlation coefficient is essential. In this context, a negative correlation suggests that there might be a relationship between higher CEO pay ratios and lower corporate revenues. However, correlation does not imply causation. It's crucial to consider other factors that may influence corporate revenue and not solely attribute changes to CEO pay ratios.

This analysis can guide further investigation into the underlying factors affecting corporate performance. Additionally, conducting a regression analysis or considering additional variables may provide a more comprehensive understanding of the dynamics between CEO pay ratios and corporate revenue for a more robust conclusion.

Answer 2

The correlation coefficient (r) between the CEO pay ratio and corporate revenue for the given dataset is approximately 0.14 when rounded to two decimal places.

Step-by-step explanation:

To calculate the correlation coefficient (r) between the CEO pay ratio and corporate revenue, Excel or a statistical software can be used. The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the economist wants to understand if there's a strong link between CEO pay ratio and corporate revenue for 30 companies.

Using Excel's correlation function or a similar statistical tool, inputting the CEO pay ratio and corporate revenue data, the calculated correlation coefficient (r) indicates the degree and direction of association between the two variables. A value of 0.14, rounded to two decimal places, suggests a weak positive correlation between CEO pay ratio and corporate revenue for these 30 companies.

Interpreting the correlation coefficient: With a value close to zero, it indicates that there is a very weak linear relationship between the CEO pay ratio and corporate revenue. The positive sign implies a slight tendency that as CEO pay ratio increases, corporate revenue might slightly increase, but the correlation is not strong enough to imply a significant or robust relationship between these two variables across the sampled companies.