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CMA Final · Strategic Cost Management · Introduction to Tools for Data Analytics

A regression of monthly electricity cost (Y, Rs thousand) on production volume (X, thousand units) for a Chennai plant gave: Y = 50 + 4X, with a coefficient of determination R-squared of 0.81. What is the correlation coefficient between X and Y, and what is the predicted cost at 25 thousand units?

The correlation coefficient is +0.90 and the predicted cost is Rs 150 thousand. R-squared of 0.81 gives r as its square root, 0.9, taking a positive sign because the slope is positive. Predicted cost at 25 is 50 plus 4 times 25, equal to 150.

  1. Ar = +0.90; Rs 150 thousandCorrect
  2. Br = +0.81; Rs 150 thousand
  3. Cr = +0.90; Rs 100 thousand
  4. Dr = -0.90; Rs 150 thousand

Explanation

r = square root of 0.81 = 0.9, and its sign matches the slope, which is positive (+4), so r = +0.90. Predicted Y = 50 + 4 x 25 = 150. Option 0.81 confuses R-squared with r; Rs 100 thousand omits the intercept; a negative r contradicts the positive slope.

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