The ability of a welded joint to elongate under stress is affected by the chemic

Question

The ability of a welded joint to elongate under stress is affected by the chemical composition of the weld metal. In an experiment to determine the effect of carbon content (x) on elongation (y), 39 welds were stressed until fracture, and both carbon content (in parts per thousand) and elongation (in percent) were measured. The following summary statistics were calculated (xi-2 = 0.6561 (xi-(yi-y) =3.9097 s = 4.33 19. Assuming that x and y follow a linear model, compute the estimated change in elongation due to an increase of one part per thousand in carbon content. Should we use the linear model to predict elongation from carbon content?

Explanation / Answer

In this case we should calculate pearson correlation coefficient

r = [(x - xbar) ( y - ybar) / n] / [(x -xbar)2 / n * y]

  = [-3.9097 / 39] / 0.13 * 4.3319

  = -0.178

We Should not use the linear model to predict elongation from carbon content. since correlation is not linear and weak negative correlation.

In this case the correlation coefficient (r) represents the strength of the relationship, and since it is much closer to zero than it is to one, that is what makes it a weak correlation

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