ABC chemical plant supervisor is concerned about the high reaction times, y of a batch process. He wants to examine the root cause of the problem and select a sequence of 6 previous batches at different concentration of impurities, x. From these data the following are calculated. ∑x=200 ∑y=436 ∑xy=12515 ∑x2=7250 ∑y2=39234 n=6 1) Compute the value of the correlation coefficient between the y and x for the given data. 2) Interpret the result obtained from part (i). 3) Comment on the suggestion that high reaction times are caused by concentration of impurities.

Question

ABC chemical plant supervisor is concerned about the high reaction times, y of a batch process. He wants to examine the root cause of the problem and select a sequence of 6 previous batches at different concentration of impurities, x. From these data the following are calculated.  ∑x=200  ∑y=436  ∑xy=12515  ∑x2=7250  ∑y2=39234  n=6  1) Compute the value of the correlation coefficient between the y and x for the given data.  2) Interpret the result obtained from part (i).  3) Comment on the suggestion that high reaction times are caused by concentration of impurities.

Befory · Accepted Answer

Step 1  ∑x=200,∑y=436,∑xy=12515  ∑x2=7250,∑y2=39234,n=6  Step 2  1) The correlation coefficient is,  r=n(∑xy)−∑x∑yn(∑x2)−(∑x)2×n(∑y2)−(∑y)2  =6(12515)−(200)(436)6(7250)−(200)2×6(39234)−(436)2  =−0.962  2) The negative value of correlation coefficient indicates that there is a negative relationship between two variables. Thus, it could be said that two variables are negatively correlated.   3) No we cannot concluded that high rate time has been caused by concentration of impurities because correlation does not imply causation

ABC chemical plant supervisor is concerned about the high reaction tim

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