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Transcript

Coefficient of Determination R2 P. 227 43,44,47 P. 2239 49,50,53 Gas chromatography is a technique used to detect very small amounts of a substance, for example, a contaminant in drinking water. Laboratories use regression to calibrate such techniques. The data below show the results of five measurements for each of four amounts of the substance being investigated. The explanatory variable x is the amount of the substance in the specimen, measure in nanograms (10 -9 gram). The response variable is the reading from the gas chromatograph. S Amount Reading on (mg) Chromatograph .25 6.25 7.98 6.54 6.37 7.96 1.00 29.7 30.0 30.1 29.5 29.1 5.00 211 204 212 213 205 20.00 929 905 922 928 919 Percent Change = (a – b) /a Difference Between R and R2 R measures strength and direction of a linear relationship. R is used to decide how well a linear model fits the data. R2 measures the percent of variation in the observed y-values that is explained by the linear regression of (y-values) on (x-values). R2 is used to measure how well the least squares regression lines does at predicting values of the response variable y.