Question

calculator active graph the data and choose the regression that best fits the data. 3. the data shows the salary in thousands of dollars for employees given their years experience.

experience (years)	salary (thousands)
4	54
5	58
8	68
9	73
12	80
15	88

a. is the data linear, quadratic, or cubic?

b. write the equation of the regression curve. f(x)=3.137x + 42.349

c. use your equation to predict the salary if an employee with 11 years experience. f(11)=76.856 thousand dollar salary

Explanation:

Step1: Identify data type

The data shows a relationship between years of experience (independent variable $x$) and salary (dependent variable $y$). By looking at the scatter - plot or analyzing the change in $y$ with respect to $x$, we can determine the type of regression. Since the change in salary with respect to experience seems to be a constant - rate change (a straight - line relationship), the data is linear.

Step2: Write regression equation

The given regression equation is $f(x)=3.137x + 42.349$, where $x$ is the number of years of experience and $f(x)$ is the salary in thousands of dollars. This equation is in the form of a linear equation $y = mx + b$, where $m = 3.137$ is the slope (rate of change of salary per year of experience) and $b = 42.349$ is the y - intercept (salary when experience is 0).

Step3: Predict salary

To predict the salary of an employee with 11 years of experience, we substitute $x = 11$ into the equation $f(x)=3.137x + 42.349$.

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Since $f(x)$ is in thousands of dollars, the predicted salary is $\$76856$.

Answer:

a. Linear
b. $f(x)=3.137x + 42.349$
c. $\$76856$