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.
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
2 answers
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.
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.
2 answers