Using the least-squares regression
line, ŷ=-25.5+ 1.5x, what is
the residual for the data point at
(28, 19)?
2.5
4.33
0-2.5
O 19
16.5



Answer :

To calculate the residual for the data point (28, 19) using the least-squares regression line, we need to follow the steps below: 1. Use the regression equation to predict the value of y (which we denote as ŷ) for the given x-value, which in this case is 28. 2. Calculate ŷ using the equation of the line: ŷ = -25.5 + 1.5x. 3. Substitute x = 28 into the equation to compute ŷ. 4. Once we obtain the predicted value, calculate the residual by subtracting the predicted value of y (ŷ) from the actual value of y (which is given as 19). Let's perform the calculations: The predicted value of y (ŷ) is: ŷ = -25.5 + 1.5(28) ŷ = -25.5 + (1.5 * 28) ŷ = -25.5 + 42 ŷ = 16.5 Now we compute the residual: residual = actual y - predicted y residual = 19 - 16.5 residual = 2.5 Therefore, the residual for the data point (28, 19) is 2.5.