# Question 1: Regression and Correlation Coefficient Company...

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FALL 2018 OPMT-600 LESSON 5 1 Lesson 5: Creating Models of Reality Using Inductive Reasoning CREATIVITY MODELS OF REALITY Question 1: Regression and Correlation Coefficient Company officials wish to study what causes defective products to be produced. They have identified several factors that may influence the number of defects positively and negatively. They believe the number of defective parts a production worker produces each week is dependent on the hours of training they received over the years. They have randomly selected 5 workers and have looked at their hours of training and the number of defects each produced in a week. X = hours of training Y = number of defects produced in a week X Y X - ´ x Y - ´ y (X - ´ ( Y - ´ y ) (X - ´ ( Y - ´ y 10 17 20 14 30 12 40 8 50 4 Total Step 1 Think Like An EMPIRICIST Using the 5 Phases of Metric Design to Sense the Natural World to Create the Dots x ) x
FALL 2018 OPMT-600 LESSON 5 2 Step 2 Think Like a RATIONALIST: Use Reasoning to Connect the Dots. In this case mathematical/statistical reasoning is used was used to discuss this so formulas for “b” and “a”. ^ Y =bX+a b= x −´ x y y ´ ¿ ¿ x x ´ ¿ ¿ ¿ 2 ¿ ¿ ( ¿ ) ¿ ¿ ¿ a= ´ y -b ´ x a) Determine the equation of the best fitting least squares line. Thinking Symbolically Algebra is a Symbolic Language. a
POTENTIAL KNOWLEDGE CREATED BY INDUCTIVE REASONING a) Draw a scatter gram and graph the above Ŷ you have determined. Clearly indicate the slope, y intercept and range of relevancy on this graph . Looking at the straight line you’ve graphed, how well does this Thinking Visually
FALL 2018 OPMT-600 LESSON 5 3 line describe the observed relationship between Number of Defects Produced and Hours of Training? 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 16 18 20 22 b) Is the equation ^ Y = bX + a ( symbolic thinking) or the scattergram (visual thinking) more informative to you? Explain. X Y
c) Give a verbal interpretation of the slope, using the numbered value of the Slope in your Verbal interpretation.
FALL 2018 OPMT-600 LESSON 5 4