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Answer :
Word Count : 499
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Alright — let’s go step-by-step. --- ## Step 1: Identify the regression lines We have: \[ 5x - 15y = 30 \quad \text{(1)} \] \[ 10x - 20y = 15 \quad \text{(2)} \] In regression, we write them as: Regression of \(y\) on \(x\): \[ y = \bar{y} + b_{yx} (x - \bar{x}) \implies y = b_{yx} x + c_1 \] Regression of \(x\) on \(y\): \[ x = \bar{x} + b_{xy} (y - \bar{y}) \implies x = b_{xy} y + c_2 \] Here, the two given equations should be one for \(y\) on \(x\) and one for \(x\) on \(y\). Usually, we put in form \(y = a + bx\) or \(x = c + dy\). --- ### From (1): \( 5x - 15y = 30 \) \[ -15y = -5x + 30 \] \[ 15y = 5x - 30 \] \[ y = \frac{5}{15}x - \frac{30}{15} = \frac{1}{3}x
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