This fitted linear regression equation applies to questions 5 and 6. Suppose you have fit a...
This fitted linear regression equation applies to questions 5 and 6.
Suppose you have fit a linear regression equation as follows: y hat= 200 + 0.10x1 + 0.2x2 - 0.93x3
Question 5: Calculate the estimated value of y if x1 is 100, x2 is 50, and x3 is 200.
Question 6: Suppose the true value of y is equal to 40 when x1 is 100, x2 is 50, and x3 is 200. Calculate the residual.
Homework Answers
Question 5: To calculate the estimated value of y, we substitute the given values of x1, x2, and x3 into the fitted linear regression equation.
Given: x1 = 100 x2 = 50 x3 = 200
The fitted linear regression equation is: y_hat = 200 + 0.10x1 + 0.2x2 - 0.93x3
Substituting the values: y_hat = 200 + 0.10 * 100 + 0.2 * 50 - 0.93 * 200
Calculating: y_hat = 200 + 10 + 10 - 186 = 34
Therefore, the estimated value of y is 34.
Question 6: To calculate the residual, we subtract the true value of y from the estimated value of y.
Given: True value of y = 40 Estimated value of y (from Question 5) = 34
Calculating the residual: Residual = True value of y - Estimated value of y Residual = 40 - 34 = 6
Therefore, the residual is 6.
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