•Input data using the key sequence shown below. P S •The values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below. E-24 To recall this type of value: Perform this key operation: .x2 .x n .y2 .y .xy o x.n x.n-1 p y.n y.n-1 Regression coefficient A Regression coefficient B A U 1 A U 2 A U 3 A U r 1 A U r 2 A U r 3 A X 1 A X 2 A X 3 A X r 1 A X r 2 A X r 3 A X r r 1 A X r r 2 Regression calculation other than quadratic regression Correlation coefficient r m n A X r r 3 A X r r r 1 A X r r r 2 • The following table shows the key operations you should use to recall results in the case of quadratic regression. To recall this type of value: Perform this key operation: .x3 .x2y .x4 Regression coefficient C m1 m2 n A U r r 1 A U r r 2 A U r r 3 A X r r 3 A X r r r 1 A X r r r 2 A X r r r 3 • The values in the above tables can be used inside of expressions the same way you use variables. uLinear Regression • The regression formula for linear regression is: y = A + Bx. E-25 • Example: Atmospheric Pressure vs. Temperature Te m p e r ature AtmosphericPressure 10°C 1003 hPa 15°C 1005 hPa 20°C 1010 hPa 25°C 1011 hPa 30°C 1014 hPa Perform linear regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate atmospheric pressure at –5°C and temperature at 1000 hPa. Finally, calculate the coefficient of determination ( r2) and sample covariance In the REG Mode: 1(Lin) A B 1(Scl) =(Stat clear) 10 P1003 S 1. n= REG Each time you press S to register your input, the number of data input up to that point is indicated on the display (n value). 15 P 1005 S 20 P1010 S 25 P 1011 S 30 P 1014 S Regression Coefficient A = 997.4 A X r r 1 = Regression Coefficient B = 0.56 A X r r 2 = Correlation Coefficient r = 0.982607368 A X r r 3 = Atmospheric Pressure at 5°C = 994.6 E D 5 F A X r r r 2 = Temperature at 1000 hPa = 4.642857143 1000 A X r r r 1 = Coefficient of Determination = 0.965517241 A X r r 3 K = Sample Covariance = 35 E A U r 3 , A U 3 -A X 1 A X r 1 F \ E A U 3 , 1 F = E-26 u Logarithmic, Exponential, Power, and Inverse Regression •Use the same key operations as linear regression to recall results for these types of regression. • The following shows the regression formulas for each type of regression. Logarithmic Regression y A B . In x Exponential Regression y A . eB·x (In y In A + Bx) Power Regression y A . xB (In y In A + B In x) Inverse Regression y A B . 1/x uQuadratic Regression • The regression formula for quadratic regression is: y = A + Bx + Cx2 . • Example: xi yi 29 1.6 50 23.5 74 38.0 103 46.4 118 48.0 Perform quadratic regression to determine the regression formula terms for the data nearby. Next, use the regression formula to estimate the values for n (estimated value of y) for xi = 16 and m (estimated value of x) for yi = 20. In the REG Mode: r 3(Quad) A B 1(Scl) = (Stat clear) 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S 103 P 46.4 S 118 P 48.0 S Regression Coefficient A = –35.59856934 A X r r 1 = Regression Coefficient B = 1.495939413 A X r r 2 = Regression Coefficient C = –6.71629667 10–3 A X r r 3 = n when xi is 16 = –13.38291067 16 A X r r r 3 = m1 when yi is 20 = 47.14556728 20 A X r r r 1 = m2 when yi is 20 = 175.5872105 20 A X r r r 2 = E-27 Data Input Precautions • S S inputs the same data twice. •You can also input multiple entries of the same data using A G. To input the data “20 and 30” five times, for example, press 20 P 30 A G 5 S. • The above results can be obtained in any order, and not necessarily that shown above. •Precautions when editing data input for standard deviation also apply for regression calculations. • Do not use variables A through F, X, or Y to store data when performing statistical calculations. These variables are used for statistical calculation temporary memory, so any data you may have assigned to them may be replaced by other values during statistical calculations. • Entering the REG Mode and selecting a regression type (Lin, Log, Exp, Pwr, Inv, Quad) clear variables A through F, X, and Y. Changing from one regression type to another inside the REG Mode also clears these variables. Technical Information k When you have a problem...... If calculation results are not what you expect or if an error occurs, perform the following steps. 1. Press A B 2(Mode) = to initialize all modes and settings. 2. Check the formula you are working with to confirm it is correct. 3. Enter the correct mode and try performing the calculation again. If the above steps do not correct the problem, press the 5key. The calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. Make sure you always keep written copies of all important data. k Error Messages The calculator is locked up while an error message is on the display. Press t to clear the error, or press e ...
