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.
you need the table in order to do the question.
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.
(Points: 6)
To find the equation of linear regression for the given data and obtain the expected salary for an electrical engineer with 48 years of experience, you need to perform a linear regression analysis on the data points. Linear regression helps in finding the best-fitting line that minimizes the distance between the observed data points and the predicted values.
Assuming you have the data points represented by (years of experience, salary), you can follow these steps:
Step 1: Calculate the mean of the years of experience (X̅) and the mean of the salaries (Y̅).
Step 2: Calculate the difference between each year of experience (X) and the mean of years of experience (X̅), and denote it by (X - X̅).
Step 3: Calculate the difference between each salary (Y) and the mean of salaries (Y̅), and denote it by (Y - Y̅).
Step 4: Calculate the product of the differences calculated in Step 2 and Step 3, denoted by (X - X̅)(Y - Y̅).
Step 5: Calculate the squared difference of each year of experience (X - X̅), denoted by (X - X̅)^2.
Step 6: Calculate the sum of the squared differences calculated in Step 5.
Step 7: Calculate the sum of the products calculated in Step 4.
Step 8: Calculate the slope of the regression line (b) using the formula b = (sum of products)/(sum of squared differences).
Step 9: Calculate the y-intercept of the regression line (a) using the formula a = Y̅ - b * X̅.
Step 10: Write the equation of the regression line in the form Ŷ = a + bX, where Ŷ is the predicted salary and X is the number of years of experience.
Step 11: Substitute the value of X = 48 into the equation obtained from Step 10 to find the expected salary for an electrical engineer with 48 years of experience.
By following these steps, you should be able to obtain the equation of linear regression and determine the expected salary for an engineer with 48 years of experience.