Question

a manager at an insurance company wishes to examine the relationship between years of college completed and the starting salary at their company. their research discovers a linear relationship, and the least squares line is: $hat{y}=46.054 + 3.6x$ where $x$ is the number of years of college completed and $y$ is the starting salary in thousands of dollars.
a) the slope of the regression line can be interpreted in the following way:
○ when amount of college increases by one year, the starting salary increases by 46.054 thousand dollars.
○ when amount of college increases by one year, the starting salary increases by 3.6 thousand dollars.
○ when amount of college increases by one year, the starting salary decreases by 46.054 thousand dollars.
○ when amount of college increases by 3.6 years, the starting salary increases by 46.054 thousand dollars.
○ when starting salary goes up by 46.054 thousand dollars, the number of years of college is 3.6.
○ when amount of college increases by one year, the starting salary decreases by 3.6 thousand dollars.
b) predict the starting salary for a person with 6 years of college. round answer to 4 decimal places.
thousand dollars.

Explanation:

Step1: Interpret the slope

The general form of a linear regression line is $\hat{y}=a + bx$, where $b$ is the slope. In the given equation $\hat{y}=46.054 + 3.6x$, the slope $b = 3.6$. The slope represents the change in $y$ (starting - salary in thousands of dollars) for a unit - change in $x$ (years of college). So, when $x$ (amount of college) increases by 1 year, $y$ (starting salary) changes by $b$ units. Since $b = 3.6>0$, when the amount of college increases by one year, the starting salary increases by 3.6 thousand dollars.

Step2: Predict the salary

We are given the regression equation $\hat{y}=46.054+3.6x$. To predict the starting salary for $x = 6$ years of college, we substitute $x = 6$ into the equation.

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Answer:

a) When amount of college increases by one year, the starting salary increases by 3.6 thousand dollars.
b) 67.6540 thousand dollars.