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 48 years of experience. Round to the nearest $100
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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 15 years of experience. Round to the nearest $100.
To find the equation of linear regression and the expected salary for an engineer with 48 years of experience, we can follow these steps:
1. Collect the data: The given data is the annual salary of electrical engineers in terms of years of experience. Please provide the data so that we can proceed with the calculations.
2. Plot the data: Using the collected data points, plot a scatter plot of years of experience (X-axis) versus annual salary (Y-axis) on a graph.
3. Calculate the regression line: The linear regression equation will help us find the expected salary for an engineer with 48 years of experience. By fitting a straight line to the data points, we can determine the equation using the least squares method. This equation is in the form of Y = aX + b, where X represents years of experience and Y represents the annual salary.
4. Find the coefficients: Calculate the values of 'a' and 'b' in the equation by using formulas:
a = (NΣXY - ΣXΣY) / (NΣX^2 - (ΣX)^2) and b = (ΣY - aΣX) / N.
N is the number of data points, Σ denotes summation, X and Y represent the respective data points, and ΣX^2 represents the sum of squares of X.
5. Plug in the values: Substitute the calculated values of 'a' and 'b' into the linear regression equation.
6. Estimate the salary: To obtain the expected salary for an engineer with 48 years of experience, substitute X = 48 into the equation and solve for Y. Round the answer to the nearest $100.
Please provide the data points so that we can proceed with the calculations.