SOLUTION: The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12

Question 1183105: The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. The best statistical test to use to reach a conclusion would be the _________.
Select one:
a. t test
b. paired t-test
c. correlation coefficient
d. simple regression
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
The best statistical test to use in this scenario is **d. simple regression**.
Here's why:
* **Simple regression** is used to model the relationship between two continuous variables: an independent variable (predictor) and a dependent variable (outcome). In this case:
* Independent variable: Number of new clients
* Dependent variable: Sales amount
The managers want to see if the number of new clients *affects* sales, suggesting a cause-and-effect relationship that regression analysis is designed to explore. Regression will allow them to quantify this relationship (how much does sales increase for each new client?), and test if the relationship is statistically significant.
Here's why the other options are less suitable:
* **t-test:** A t-test is used to compare the means of two groups. This scenario doesn't involve comparing groups; it's about examining the relationship between two continuous variables.
* **paired t-test:** A paired t-test is used when you have two related samples (e.g., measurements taken before and after an intervention on the *same* individuals). This isn't the case here.
* **correlation coefficient:** While the correlation coefficient measures the *strength* and *direction* of a linear relationship, it doesn't provide a model for how one variable *affects* the other. It simply tells you if they tend to move together. Regression analysis goes a step further by creating a predictive model and quantifying the impact.

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