The annual Salary of an electrical engineer is given in terms of the years of experience by the table below. Find the equation of linear regression for the above data and obtain the expected salary for an engineer with 45 years of experience. Round to the nearest $100.
Years of Experience
2
5
9
14
19
23
28
33
36
Annual Salary in $1000’s
53.5
56.3
59.8
63
65.6
69.5
75
76
84
a) 97,000
b) 88,300
c) 56,700
d) 92,800
If you need to show the work by hand, you can develop the regression equation in the following format:
predicted y = a + bx
...where a represents the y-intercept and b the slope.
To get to that point, here are some formulas to calculate along the way.
To find a:
a = (Ey/n) - b(Ex/n)
Note: E here means to add up or to find the total.
To find b:
b = SSxy/SSxx
To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n
To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n
Once you have the equation, substitute 45 for x and solve for predicted y.
I hope this will help get you started.
Q: The mean annual salary for a sample of electrical engineers is $83,500, with a standard deviation
The mean annual salary for a sample of electrical engineers is $83,500, with a standard deviation of $1500. The data set has a bell-shaped distribution.
(a) Use the Empirical Rule to estimate the percent of electrical engineers whose annual salaries are between $80,500 and $86,500.
(b) In a sample of 40 additional electrical engineers, about how many electrical engineers would you expect to have annual salaries between $80,500 and $86,500?
(c) The salaries of three randomly selected electrical engineers are $90,500, $79,750, and $82,600. Find the z-score that corresponds to each salary. Determine whether any of these salaries are unusual.
To find the equation of linear regression, we need to determine the relationship between the years of experience and the annual salary.
First, let's plot the data points on a scatter plot to visualize the relationship between the variables.
Years of Experience (x-axis) Annual Salary in $1000’s (y-axis)
2 53.5
5 56.3
9 59.8
14 63
19 65.6
23 69.5
28 75
33 76
36 84
Next, we can calculate the equation of a linear regression line that best fits the data. This line is represented by the equation: y = mx + c, where y is the annual salary, x is the years of experience, m is the slope, and c is the y-intercept.
Using a statistical software or spreadsheet program, we can calculate the linear regression line. The equation is given as follows:
y = 1.8727x + 50.0909
Now we can substitute x = 45 (years of experience) into the equation to find the expected salary:
y = 1.8727 * 45 + 50.0909
y ≈ 92,799.87
Rounding to the nearest $100, the expected salary for an engineer with 45 years of experience is $92,800.
Therefore, the correct answer is: (d) 92,800.