The General Manager of a Chain of Furniture Stores Believes

question 53

Essay

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. Determine the standard error of estimate.
s_r = ______________
Describe what this statistic tells you about the regression line.
______________
Determine the coefficient of determination.
R² = ______________
Discuss what its value tells you about the two variables.
______________
Calculate the Pearson correlation coefficient.
r = ______________
Why does it have the sign it has?
______________
Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales.
Test statistic:
t = ______________
Rejection Region:
Reject H₀ if | t | > ______________
Conclusion:
______________
A linear relationship ______________ between years of experience and sales.

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Definitions:

Confidence Interval

An estimate of an interval in statistics that likely contains a population parameter, providing a range of plausible values for that parameter.

Average Value

The sum of a set of numerical values divided by the number of values in the set, commonly referred to as the mean.

Simple Linear Regression

A statistical method for modeling the relationship between a single independent variable and a dependent variable by fitting a linear equation to observed data.

Correlation Coefficient

A numerical measure that quantifies the degree to which two variables are related or move together.