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.

x y
2 51.5
5 56.3
9 61
14 63
19 66
24 69.5
24 73
28 76
32 84

To find the equation of linear regression for the given data and obtain the expected salary for an engineer with 45 years of experience, we can follow these steps:

Step 1: Calculate the means of the x-values and y-values.
The mean of the x-values (years of experience) is calculated by summing all the x-values and dividing by the total number of data points:
mean(x) = (2+5+9+14+19+24+24+28+32) / 9 = 20.

The mean of the y-values (annual salary) is calculated by summing all the y-values and dividing by the total number of data points:
mean(y) = (51.5+56.3+61+63+66+69.5+73+76+84) / 9 = 66.16.

Step 2: Calculate the deviations from the means.
For each x-value, subtract the mean of x (20) from the respective x-value to get the deviation from the mean of x.
For each y-value, subtract the mean of y (66.16) from the respective y-value to get the deviation from the mean of y.
Let's call the deviations from the means as dx and dy.

The deviations from the means:
dx = (-18,-15,-11,-6,-1,4,4,8,12)
dy = (-14.66, -9.86, -5.16, -3.16, -0.16, 3.34, 6.84, 9.84, 17.84)

Step 3: Calculate the sum of squared deviations.
For each pair of deviations (dx, dy), calculate the square of each deviation, and sum them up.
Let's call the sum of squared deviations as SSxx and SSxy.

The sum of squares for the x-values:
SSxx = (-18)^2 + (-15)^2 + (-11)^2 + (-6)^2 + (-1)^2 + 4^2 + 4^2 + 8^2 + 12^2 = 946.

The sum of product of deviations:
SSxy = (-18) * (-14.66) + (-15) * (-9.86) + (-11) * (-5.16) + (-6) * (-3.16) + (-1) * (-0.16) + 4 * 3.34 + 4 * 6.84 + 8 * 9.84 + 12 * 17.84 = 2,471.1.

Step 4: Calculate the slope and y-intercept of the linear regression line.
The slope (b) is calculated by dividing the sum of product of deviations (SSxy) by the sum of squares of x-values (SSxx):
b = SSxy / SSxx = 2471.1 / 946 = 2.6162 (rounded to four decimal places).

The y-intercept (a) is calculated by subtracting the product of the slope (b) and the mean of x-values (mean(x)) from the mean of y-values (mean(y)):
a = mean(y) - (b * mean(x)) = 66.16 - (2.6162 * 20) = 16.84.

Step 5: Write the equation of linear regression.
The equation of linear regression is given by y = a + b * x, where y is the expected annual salary and x is the years of experience.

The equation of linear regression for the given data is:
y = 16.84 + 2.6162 * x.

Step 6: Obtain the expected salary for an engineer with 45 years of experience.
Substitute x = 45 in the equation of linear regression to find y:
y = 16.84 + 2.6162 * 45 = 16.84 + 118.226 = 135.066 (rounded to three decimal places).
Therefore, the expected salary for an engineer with 45 years of experience is $135,066 (rounded to the nearest $100).

To summarize, the equation of linear regression is y = 16.84 + 2.6162 * x, and the expected salary for an engineer with 45 years of experience is $135,066 (rounded to the nearest $100).