As an analyst of firms characteristics and profitability, you are considering the relationship between firm profitability and the amount paid to their CEOs. A simple random sample of 121 firms was collected and data on the following two variables obtained:

Profiti= Annual profit of firmiin millions of dollars

Salaryi= Salary of the CEO in millions of dollars

A regression ofProfitionSalaryiis estimated, given the following equation, (with standard errors in brackets):

(

Profiti|Salaryi) =-0.141+0.287Salaryi(0.071)(0.047)

Use these results to answer the following questions.

1. (2 marks) Give an interpretation of the coefficient onSalaryi
2. (2 marks) Construct a 95% confidence interval for the population coefficient onSalaryiin this equation. Give the critical value as well as the confidence interval.
3. (3 marks) Your boss claims there should be some statistical relationship between firm profitability and CEO salary. Use your previous answer to evaluate this claim.
4. (3 marks) Your boss further claims that paying a CEO a higher salary will cause the CEO to perform better and hence produce higher firm profitability. Is this claim confirmed by the regression results? Explain.
5. (2 marks) TheR2for the regression is 0.236. What does this measure and what are its implications for this regression?
6. (3 marks) Consider the scatter plot below ofProfitiandSalaryi. What do you observe about this plot that might be a problem for statistical inference in the regression? Explain.