Linear Regression Statistics Example 3

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Example 3

hard
A regression equation is y^=50−2.3x\hat{y} = 50 - 2.3x. Interpret the slope. If x=8x = 8, find y^\hat{y}.

Solution

  1. 1
    Step 1: Slope = −2.3: for each unit increase in xx, y^\hat{y} decreases by 2.3.
  2. 2
    Step 2: y^=50−2.3(8)=50−18.4=31.6\hat{y} = 50 - 2.3(8) = 50 - 18.4 = 31.6.

Answer

Slope: yy decreases by 2.3 per unit increase in xx. y^=31.6\hat{y} = 31.6 when x=8x = 8.
A negative slope indicates an inverse relationship: as xx increases, the predicted yy decreases.

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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