HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 583

Type of Fitting Linear Log. Exp. Power Actual Model Linearized Model y = a + bx [same] y = a + b ln(x) [same] y = a ebx ln(y) = ln(a) + bx y = a xb ln(y) = ln(a) + b ln(x) Indep. variable ξ x ln(x) x ln(x) Depend. Variable η y Covar. sξη sxy y sln(x),y ln(y) sx,ln(y) ln(y) sln(x),ln(y) ∑ The sample covariance of ξ,η is given by sξη = 1 n −1 (ξi − ξ )(ηi −η ) Also, we define the sample variances of ξ and η, respectively, as ∑ s ξ2 = 1 n −1 n i =1 (ξ i −ξ )2 ∑ s η2 = 1 n −1 n i =1 (ηi −η )2 The sample correlation coefficient rξη is rξη = sξη sξ ⋅ sη The general form of the regression equation is η = A + Bξ. Best data fitting The calculator can determine which one of its linear or linearized relationship offers the best fitting for a set of (x,y) data points. We will illustrate the use of this feature with an example. Suppose you want to find which one of the data fitting functions provides the best fit for the following data: x 0.2 0.5 1 1.5 2 4 5 10 y 3.16 2.73 2.12 1.65 1.29 0.47 0.29 0.01 First, enter the data as a matrix, either by using the Matrix Writer and entering the data, or by entering two lists of data corresponding to x and y and using Page 18-12