Linear Regression Statistics Example 4

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Example 4

hard
A regression line is y^=4+1.5x\hat{y} = 4 + 1.5x. Predict yy when x=12x = 12, and decide whether this is interpolation if the observed x-values ranged from 5 to 15.

Solution

  1. 1
    Step 1: Substitute x=12x = 12: y^=4+1.5(12)=4+18=22\hat{y} = 4 + 1.5(12) = 4 + 18 = 22.
  2. 2
    Step 2: Since 12 lies within the observed range 5 to 15, this prediction is interpolation, not extrapolation.

Answer

y^=22\hat{y} = 22, and the prediction is interpolation.
Regression predictions are safer within the range of observed data. Interpolation uses the model inside the data range, while extrapolation extends beyond it and is more risky.

About Linear Regression

Linear regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a straight line that minimizes the sum of squared distances from data points to the line (least squares method).

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