{"id":1566,"date":"2023-07-25T20:42:10","date_gmt":"2023-07-25T20:42:10","guid":{"rendered":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-power-regression\/"},"modified":"2023-07-25T20:42:10","modified_gmt":"2023-07-25T20:42:10","slug":"r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-power-regression","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-power-regression\/","title":{"rendered":"R \u1016\u103c\u1004\u1037\u103a \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038 (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Power regression<\/strong> \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1015\u102f\u1036\u1005\u1036\u1016\u103c\u1004\u1037\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c linear \u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = <sup>axb<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>y-<\/strong> \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x-<\/strong> \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>a, b-<\/strong> <em>x<\/em> \u1014\u103e\u1004\u1037\u103a <em>y<\/em> \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1021\u102c\u1038 \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f <a href=\"https:\/\/statorials.org\/my\/\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c-\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a-\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/a> \u101e\u100a\u103a \u1015\u102b\u101d\u102b\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u1019\u103c\u103e\u1004\u1037\u103a\u1010\u1004\u103a\u1015\u1031\u1038\u101e\u100a\u1037\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u1037\u103a \u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1036\u1015\u103c\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1021\u1010\u103d\u1000\u103a \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a x \u1014\u103e\u1004\u1037\u103a y \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data<\/span>\nx=1:20\ny=c(1, 8, 5, 7, 6, 20, 15, 19, 23, 37, 33, 38, 49, 50, 56, 52, 70, 89, 97, 115)<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a x \u1014\u103e\u1004\u1037\u103a y \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a scatterplot \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot<\/span>\nplot(x, y)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15543 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/puissancer1.png\" alt=\"\" width=\"450\" height=\"416\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1002\u101b\u1015\u103a\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1015\u103c\u1010\u103a\u101e\u102c\u1038\u101e\u1031\u102c \u1015\u102b\u101d\u102b\u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1015\u103c\u101e\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a linear regression model \u1011\u1000\u103a data \u1014\u103e\u1004\u1037\u103a power regression equation \u1000\u102d\u102f \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1015\u102f\u1036\u101b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a R \u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u101f\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1000\u102c \u1012\u1031\u1010\u102c\u1014\u103e\u1004\u1037\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a <strong>lm()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the model\n<\/span>model &lt;- lm(log(y)~ log(x))\n\n<span style=\"color: #008080;\">#view the output of the model\n<\/span>summary(model)\n\nCall:\nlm(formula = log(y) ~ log(x))\n\nResiduals:\n     Min 1Q Median 3Q Max \n-0.67014 -0.17190 -0.05341 0.16343 0.93186 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 0.15333 0.20332 0.754 0.461    \nlog(x) 1.43439 0.08996 15.945 4.62e-12 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.3187 on 18 degrees of freedom\nMultiple R-squared: 0.9339, Adjusted R-squared: 0.9302 \nF-statistic: 254.2 on 1 and 18 DF, p-value: 4.619e-12<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a <a href=\"https:\/\/statorials.org\/my\/\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a-\u1021\u101c\u102f\u1036\u1038\u1005\u102f\u1036\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a-f-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f-\u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a-\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u1010\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u104f F-value<\/a> \u101e\u100a\u103a 252.1 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-value \u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1014\u102d\u1019\u1037\u103a\u1014\u1031\u1015\u102b\u101e\u100a\u103a (4.619e-12)\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">output table \u1019\u103e coefficients \u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d fitted power regression equation \u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ln(y) = 0.15333 + 1.43439ln(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>e \u1000\u102d\u102f<\/em> \u1014\u103e\u1005\u103a\u1016\u1000\u103a\u1005\u101c\u102f\u1036\u1038\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1015\u103c\u1014\u103a\u101c\u100a\u103a\u101b\u1031\u1038\u101e\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>y = e <sup>0.15333 + 1.43439ln(x)<\/sup><\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y = 1.1657x <sup>1.43439<\/sup><\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u104a <em>x<\/em> \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a <em>y<\/em> \u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101b\u1014\u103a \u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u104a <em>x<\/em> = 12 \u1006\u102d\u102f\u101b\u1004\u103a <em>y<\/em> \u1000 <strong>41.167<\/strong> \u1016\u103c\u1005\u103a\u1019\u101a\u103a \u104a<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 1.1657(12) <sup>1.43439<\/sup> = 41.167<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1015\u102d\u102f\u1006\u102f-<\/strong> \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f variable \u1021\u1010\u103d\u1000\u103a \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1024\u1021\u103d\u1014\u103a\u101c\u102d\u102f\u1004\u103a\u1038\u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/my\/multiple-linear-regression-r\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a linear regression \u1021\u1019\u103b\u102c\u1038\u1021\u1015\u103c\u102c\u1038\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-exponential-regression\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a exponential regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-logarithmic-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a \u101c\u1031\u102c\u1037\u1002\u101b\u1005\u103a\u101e\u1019\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Power regression \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1015\u102f\u1036\u1005\u1036\u1016\u103c\u1004\u1037\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c linear \u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b y = axb \u101b\u103d\u103e\u1031- y- \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a x- \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a a, b- x \u1014\u103e\u1004\u1037\u103a y \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038 \u1024\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1021\u102c\u1038 \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u101e\u100a\u103a \u1015\u102b\u101d\u102b\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u1019\u103c\u103e\u1004\u1037\u103a\u1010\u1004\u103a\u1015\u1031\u1038\u101e\u100a\u1037\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u1037\u103a \u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1036\u1015\u103c\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1021\u1010\u103d\u1000\u103a \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b \u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a x \u1014\u103e\u1004\u1037\u103a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R \u1016\u103c\u1004\u1037\u103a \u1015\u102b\u101d\u102b\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f 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