Question

n a linear regression of sales (measured in millions of dollars) on number of employees for 120 medium-sized firms, the fitted regression line is Sales_hat = 5.02 + 0.21*Employees. ECO220, Inc., which has 240 employees and sales of $43.2 million, is the 20th observation in the data. What is the value of the residual for ECO220, Inc., e20, in millions of dollars? Give your answer to two decimal places. (Reminder: you are being asked for a single residual, not for the sum of squared residuals).

Answer 1

solution:

Given regression line is

Sales_hat = 5.02 + 0.21 * Employees

Given that company ECO220 Inc which has 240 employees had sales of $43.2 million

So the observed value of Sales = $43.2 million

The predicted value of Sales which is Sales_hat = 5.02 + 0.21 * 240

= 5.02 + 50.4

= 55.42 million

Residual = Observed value of Sales - Predicted value of Sales

= $43.2 million - $55.42 million

= -12.22 million

So Residual for ECO220 Inc = 12.22 million

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