# 10-Error_5.web - Acomplicatedtheory(and )behind simplesteps...

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A complicated theory (and  advanced understanding) behind  simple steps Use tabulated information!

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Table 2. Critical values of Student’s- t .  The number of degrees of  freedom  ν  = n -1 Degrees of freedom t at a confidence level of 90% 95% 99% 1 6.314 12.706 63.657 2 2.920 4.303 9.925 3 2.353 3.182 5.841 4 2.132 2.776 4.604 5 2.015 2.571 4.032 6 1.943 2.447 3.707 7 1.895 2.365 3.500 8 1.860 2.306 3.355 9 1.833 2.262 3.250 10 1.812 2.228 3.169 15 1.753 2.131 2.947 20 1.725 2.086 2.845 25 1.708 2.068 2.787 30 1.697 2.042 2.750 40 1.684 2.021 2.704 60 1.671 2.000 2.660 1.645 1.960 2.576
The number of degrees of  freedom  ν  = n -1

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LINEAR REGRESSION (variables: y and x) A line will be the best straight line drawn through the data ( x i ,y i ) when the sum of squares of the vertical deviations between the data points and the line (squares of “residuals”) is minimized. y depends on x! Data scatter around the “best straight line”? A set of ( x i , y i ) data (data pairs) yields a straight line fit: y = mx + c where m is the slope, and c is the intercept. We will first look at the distance vs. time and next electrolysis mass vs. time plots . Harris pages: 83 – 95; use of a scientific calculator, or Excel spreadsheet function “linest”. “The Method of Least Squares” and “Calibration Curves”.
One minimizes the expression: y i y i i i n - = = 2 1 assuming the linear fit through individual points i is: c i mx + = i y ˆ The form for differentiation is (by substitution): y i mx i c i i n - - = = 2 1 the differentiation is performed with respect to m and c.

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the least-squares method of the data treatment. The product is “the best straight line”. How good is the best straight line is expressed by the coefficient of determination, r 2 (the square of the correlation coefficient) . The closer to unity is r 2 the better the fit. In practice, r 2 smaller than 0.9 makes the fitting procedure to a straight line unreliable. A higher order fit should then be considered (binomial or polynomial). A set of equations resulting from bringing the derivatives to
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10-Error_5.web - Acomplicatedtheory(and )behind simplesteps...

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