measurement processes for that they use a set of Known xs to

measurement processes, for that they use a set of Known x\'s to obtain observed Y\'s, then fit a model called the calibration model and use this model to convert future measured Y\'s back into the corresponding X\'s. The following is an example taken from analytical chemistry where the process is the assay of the element calcium. Determining calcium in the presence of other elements is quite tricky. The following table records the quantities of calcium in carefully prepared solutions (X) and the corresponding analytical results (Y): X: 4 8 12.5 16 20 25 31 36 40 40 Y: 3.7 7.8 12.1 15.6 19.8 24.5 31.1 35.5 39.4 39.5 Summary values: sigma X = 232.5, sigma Y = 229, sigma X^2 = 6974, sigma Y^2 = 6796.66, sigma XY = 6884.65 Fit a simple linear regression of Y as a function of X. List the assumptions that you make and interpret the coefficients. Calculate a 95% confidence interval for the intercept of your model and interpret. Calculate a 95% confidence interval for the slope of your model and interpret. In this context, two properties may he expected: When X=0, then Y=0, if there is no calcium present, your technique should not find any. If the empirical technique is any good at all, then the slope in the simple linear regression should be 1. Is there evidence for i), for ii)? - Discuss thoroughly with supportive data

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