A Sample of 30 Companies Was Randomly Selected for a Study

question 5

Essay

A sample of 30 companies was randomly selected for a study investigating what factors affect the size of company bonuses. Data were collected on the number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). Below are the multiple regression results. a. Write out the estimated regression equation.
b. Are all of the independent variables significant in this regression equation (using α = 0 .05)? Explain.
c. Interpret the coefficient of the Union.
d. Based on the scatterplot below, do you think using Union as an indicator variable in this model is appropriate? Explain. e. An alternative multiple regression model is fit to these data and the results are shown below. Which model is better? Explain. f. Using the better model, predict the annual average bonus for a company with 7500 employees that are not unionized.

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Definitions:

Null Hypothesis

A statement suggesting that there is no significant difference or relationship in the data being analyzed.

Critical Value

A threshold value that is compared with the test statistic to determine whether to reject the null hypothesis in hypothesis testing.

Null Hypothesis

A statement that there is no effect or no difference, and it serves as the default assumption to be tested against an alternative hypothesis in statistical analysis.

Doubled Samples

An approach in research where the sample size is increased twofold to improve the statistical power or reduce the margin of error.