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Find the equation of the regression line y=ax+b and estimate y when x=12, given a=3/5 and b=-2.

Mathematics

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Answer

y=35x−2y = \frac{3}{5}x - 2

5.2

Step-by-step solution

2 steps
  1. Determine the equation of the regression line.

    The general equation for the regression line of yy on xx is y=ax+by = ax + b.
    From the problem statement and the partial solution, we are given the gradient a=35a = \frac{3}{5} and we have calculated the y-intercept b=−2b = -2.
    Substitute these values into the equation:

    y=35x−2y = \frac{3}{5}x - 2
  2. Estimate yy when x=12x=12.

    Substitute x=12x=12 into the regression equation found in Step 1:

    y=35(12)−2y = \frac{3}{5}(12) - 2 y=365−2y = \frac{36}{5} - 2 y=7.2−2y = 7.2 - 2 y=5.2y = 5.2

    The equation of the line is y=35x−2\boxed{y = \frac{3}{5}x - 2} and the estimated value of yy when x=12x=12 is 5.2\boxed{5.2}.

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