Math Problem Statement

Find the value of X. If y = 5.36 and the regression equation is x = 3y + 6.35.

Solution

We are given the regression equation x=3y+6.35x = 3y + 6.35, and we are asked to find the value of xx when y=5.36y = 5.36.

Let's substitute y=5.36y = 5.36 into the equation and solve for xx:

x=3(5.36)+6.35x = 3(5.36) + 6.35

First, calculate 3×5.363 \times 5.36:

3×5.36=16.083 \times 5.36 = 16.08

Now, add 6.356.35 to 16.0816.08:

x=16.08+6.35=22.43x = 16.08 + 6.35 = 22.43

So, the value of xx is 22.43\boxed{22.43}, which corresponds to option D.

Would you like more details or have any further questions? Here are some related questions to deepen your understanding:

  1. What is the general form of a linear regression equation?
  2. How do you interpret the coefficients in a linear regression model?
  3. How would you solve for yy if the equation was y=3x+6.35y = 3x + 6.35 and x=5.36x = 5.36?
  4. What is the significance of the constant term 6.356.35 in the equation?
  5. Can you explain how the slope of 33 affects the relationship between xx and yy?

Tip: When solving linear equations, always check if both terms are correctly multiplied and added to avoid errors in calculations.

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Math Problem Analysis

Mathematical Concepts

Linear regression
Substitution

Formulas

x = 3y + 6.35

Theorems

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Suitable Grade Level

Grades 9-12