The residuals of the linear regression equation are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
How to determine the residuals?
The regression equation is given as:
y = 0.138x + 1.166
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 20 + 1.166 = 3.93
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 16.7 + 1.166 = 3.47
y = 0.138 * 15.5 + 1.166 = 3.31
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 3.7 - 3.65 = 0.05
Residual = 3.69 - 4.19 = -0.5
Residual = 3.8 - 3.65= 0.15
Residual = 4 - 3.93 = 0.07
Residual = 4 - 3.65= 0.35
Residual = 1.11 - 1.26 = -0.15
Residual = 3.69 - 4.19 = -0.5
Residual = 1.11 - 1.26 = -0.15
Residual = 3.5 - 3.47 = 0.03
Residual = 3.92 - 3.31 = 0.61
Hence, the residuals of the linear regression equation are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
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