{"id":454,"date":"2019-01-06T12:08:45","date_gmt":"2019-01-06T03:08:45","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/test-for-difference-between-regression-lines-in-r\/"},"modified":"2024-10-12T12:47:06","modified_gmt":"2024-10-12T03:47:06","slug":"test-for-difference-between-regression-lines-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/test-for-difference-between-regression-lines-in-r\/","title":{"rendered":"R \u3067\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n

\u4e8c\u3064\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u3042\u3063\u3066\u3001\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u304c\u63cf\u3051\u305f\u3068\u304d\u3001\u305d\u306e\u3042\u3068\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u304b\uff1f<\/p>\n\n\n\n

\u305d\u306e\u3042\u3068\u306f\u3001\u50be\u304d\u304c\u540c\u3058\u3068\u8a00\u3048\u308b\u304b\uff1f\u3055\u3089\u306b\u306f\u5207\u7247\u304c\u540c\u3058\u3068\u8a00\u3048\u308b\u304b\uff1f\u3068\u9032\u3093\u3067\u3044\u304f\u3002<\/p>\n\n\n\n

\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u3092\u691c\u5b9a\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n\n\n\n\n

\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf<\/h2>\n\n\n\n

\u30c7\u30fc\u30bf\u306f\u3053\u3061\u3089\u3002C\u5730\u533a\u3068O\u5730\u533a\u306eNO2\u6fc3\u5ea6\uff08X\uff09\u3068\u305b\u304d\u30fb\u305f\u3093\u6709\u75c7\u5272\u5408\uff08Y\uff09\u306e\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n

NO2.c <-<\/span> c<\/span>(<\/span>0.025<\/span>,<\/span>0.030<\/span>,<\/span>0.016<\/span>,<\/span>0.028<\/span>,<\/span>0.021<\/span>,<\/span>0.041<\/span>,<\/span>0.012<\/span>,<\/span>0.015<\/span>,<\/span>0.030<\/span>,<\/span>0.018<\/span>,<\/span>0.023<\/span>)<\/span>\npre.c <-<\/span> c<\/span>(<\/span>4.1<\/span>,<\/span>6.8<\/span>,<\/span>2.6<\/span>,<\/span>11.5<\/span>,<\/span>2.8<\/span>,<\/span>10.7<\/span>,<\/span>2.7<\/span>,<\/span>2.8<\/span>,<\/span>3.5<\/span>,<\/span>5.0<\/span>,<\/span>3.6<\/span>)<\/span>\nare.c <-<\/span> rep<\/span>(<\/span>\"c\"<\/span>,<\/span>length<\/span>(<\/span>NO2.c))<\/span>\nNO2.o <-<\/span> c<\/span>(<\/span>0.024<\/span>,<\/span>0.033<\/span>,<\/span>0.030<\/span>,<\/span>0.017<\/span>,<\/span>0.022<\/span>,<\/span>0.027<\/span>,<\/span>0.016<\/span>,<\/span>0.017<\/span>,<\/span>0.020<\/span>,<\/span>0.022<\/span>)<\/span>\npre.o <-<\/span> c<\/span>(<\/span>6.8<\/span>,<\/span>8.7<\/span>,<\/span>11.4<\/span>,<\/span>4.5<\/span>,<\/span>5.6<\/span>,<\/span>10.5<\/span>,<\/span>5.2<\/span>,<\/span>6.8<\/span>,<\/span>6.0<\/span>,<\/span>8.0<\/span>)<\/span>\nare.o <-<\/span> rep<\/span>(<\/span>\"o\"<\/span>,<\/span>length<\/span>(<\/span>NO2.o))<\/span>\n<\/code><\/pre>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\u306e\u524d\u306b\u307e\u305a\u6563\u5e03\u56f3\u3092\u63cf\u3044\u3066\u307f\u308b<\/h2>\n\n\n\n
\u6563\u5e03\u56f3\u3092\u63cf\u304f\u306b\u306fplot()\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
O\u5730\u533a\u306f\u3001points()\u3092\u4f7f\u3063\u3066\u3001\u4e09\u89d2\uff08pch=2\uff09\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
plot<\/span>(<\/span>NO2.c,<\/span> pre.c,<\/span> las=<\/span>1<\/span>,<\/span> xlim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.05<\/span>),<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>12<\/span>),<\/span>\nxlab=<\/span>\"Annual average of NO2 concentration\"<\/span>,<\/span>\nylab=<\/span>\"Prevalence of cough and\/or sputum (%)\"<\/span>)<\/span>\ntitle<\/span>(<\/span>\" Difference between two regression lines \"<\/span>)<\/span>\npoints<\/span>(<\/span>NO2.o,<\/span> pre.o,<\/span> pch=<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u56de\u5e30\u76f4\u7dda\u3092\u6c42\u3081\u3066\u307f\u308b<\/h2>\n\n\n\n
function(){} \u3067\u81ea\u4f5c\u3057\u305f\u95a2\u6570\u3067\u56de\u5e30\u76f4\u7dda\u306e\u50be\u304d\u3068\u5207\u7247\u3092\u6c42\u3081\u308b\u3002<\/p>\n\n\n\n
linear.reg <-<\/span> function<\/span>(<\/span>x,<\/span>y){<\/span>\nxbar <-<\/span> mean<\/span>(<\/span>x)<\/span>\nybar <-<\/span> mean<\/span>(<\/span>y)<\/span>\nn <-<\/span> length<\/span>(<\/span>x)<\/span>\nb <-<\/span> sum<\/span>((<\/span>x-<\/span>xbar)<\/span>*<\/span>(<\/span>y-<\/span>ybar))<\/span>\/<\/span>sum<\/span>((<\/span>x-<\/span>xbar)<\/span>^<\/span>2<\/span>)<\/span>\na <-<\/span> ybar-<\/span>b*<\/span>xbar\nyhat <-<\/span> a+<\/span>b*<\/span>x\nR2 <-<\/span> sum<\/span>((<\/span>yhat-<\/span>ybar)<\/span>^<\/span>2<\/span>)<\/span>\/<\/span>sum<\/span>((<\/span>y-<\/span>ybar)<\/span>^<\/span>2<\/span>)<\/span>\nVE <-<\/span> 1<\/span>\/<\/span>(<\/span>n-<\/span>2<\/span>)<\/span>*<\/span>sum<\/span>((<\/span>y-<\/span>(<\/span>a+<\/span>b*<\/span>x))<\/span>^<\/span>2<\/span>)<\/span>\nrse <-<\/span> sqrt<\/span>(<\/span>VE)<\/span>\nSEb <-<\/span> sqrt<\/span>(<\/span>VE\/<\/span>sum<\/span>((<\/span>x-<\/span>xbar)<\/span>^<\/span>2<\/span>))<\/span>\nTb <-<\/span> b\/<\/span>SEb\npb <-<\/span> 2<\/span>*<\/span>pt<\/span>(<\/span>abs<\/span>(<\/span>Tb),<\/span> n-<\/span>2<\/span>,<\/span> lower.tail=<\/span>F<\/span>)<\/span>\nbl <-<\/span> b-<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> n-<\/span>2<\/span>)<\/span>*<\/span>SEb\nbu <-<\/span> b+<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> n-<\/span>2<\/span>)<\/span>*<\/span>SEb\nSEa <-<\/span> sqrt<\/span>(<\/span>VE*<\/span>(<\/span>1<\/span>\/<\/span>n+<\/span>xbar^<\/span>2<\/span>\/<\/span>sum<\/span>((<\/span>x-<\/span>xbar)<\/span>^<\/span>2<\/span>)))<\/span>\nTa <-<\/span> a\/<\/span>SEa\npa <-<\/span> 2<\/span>*<\/span>pt<\/span>(<\/span>abs<\/span>(<\/span>Ta),<\/span> n-<\/span>2<\/span>,<\/span> lower.tail=<\/span>F<\/span>)<\/span>\nal <-<\/span> a-<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> n-<\/span>2<\/span>)<\/span>*<\/span>SEa\nau <-<\/span> a+<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> n-<\/span>2<\/span>)<\/span>*<\/span>SEa\nlist<\/span>(<\/span>\nc<\/span>(<\/span>Slope=<\/span>b,<\/span>\"t_Slope\"<\/span>=<\/span>Tb,<\/span> \"p_Slope\"<\/span>=<\/span>pb,<\/span> \"LL_Slope\"<\/span>=<\/span>bl,<\/span> \"UL_Slope\"<\/span>=<\/span>bu,<\/span>\nIntercept=<\/span>a,<\/span>\"t_Intcp\"<\/span>=<\/span>Ta,<\/span> \"p_Intcp\"<\/span>=<\/span>pa,<\/span> \"LL_Intcp\"<\/span>=<\/span>al,<\/span> \"UL_Intcp\"<\/span>=<\/span>au,<\/span>\n\"Error Var.\"<\/span>=<\/span>VE,<\/span>\"Resid. SE\"<\/span>=<\/span>rse,<\/span>\"R^2\"<\/span>=<\/span>R2))<\/span>\n}<\/span>\nlinear.reg<\/span>(<\/span>x=<\/span>NO2.c,<\/span> y=<\/span>pre.c)<\/span>\nlinear.reg<\/span>(<\/span>x=<\/span>NO2.o,<\/span> y=<\/span>pre.o)<\/span>\nlinreg.c <-<\/span> unlist<\/span>(<\/span>linear.reg<\/span>(<\/span>x=<\/span>NO2.c,<\/span> y=<\/span>pre.c))<\/span>\nlinreg.o <-<\/span> unlist<\/span>(<\/span>linear.reg<\/span>(<\/span>x=<\/span>NO2.o,<\/span> y=<\/span>pre.o))<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
><\/span> linear.reg<\/span>(<\/span>x=<\/span>NO2.c,<\/span> y=<\/span>pre.c)<\/span>\n[[<\/span>1<\/span>]]<\/span>\nSlope      t_Slope      p_Slope     LL_Slope     UL_Slope\n279.85418266<\/span>   3.23205342<\/span>   0.01028875<\/span>  83.98051896<\/span> 475.72784635<\/span>\nIntercept      t_Intcp      p_Intcp     LL_Intcp     UL_Intcp\n-<\/span>1.48929394<\/span>  -<\/span>0.69132430<\/span>   0.50680073<\/span>  -<\/span>6.36257401<\/span>   3.38398613<\/span>\nError Var.    Resid. SE          R^<\/span>2<\/span>\n5.32855590<\/span>   2.30836650<\/span>   0.53718391<\/span>\n><\/span> linear.reg<\/span>(<\/span>x=<\/span>NO2.o,<\/span> y=<\/span>pre.o)<\/span>\n[[<\/span>1<\/span>]]<\/span>\nSlope       t_Slope       p_Slope      LL_Slope      UL_Slope\n317.540322581<\/span>   3.780409062<\/span>   0.005385004<\/span> 123.844538638<\/span> 511.236106524<\/span>\nIntercept       t_Intcp       p_Intcp      LL_Intcp      UL_Intcp\n0.110080645<\/span>   0.055902022<\/span>   0.956790802<\/span>  -<\/span>4.430835999<\/span>   4.650997290<\/span>\nError Var.     Resid. SE           R^<\/span>2<\/span>\n2.099679940<\/span>   1.449027239<\/span>   0.641118694<\/span>\n<\/code><\/pre>\n\n\n\n
C \u5730\u533a\u3068 O \u5730\u533a\u3054\u3068\u306b\u3001Slope\uff08\u50be\u304d\uff09\u3068 Intercept\uff08\u5207\u7247\uff09\u304c\u8a08\u7b97\u3055\u308c\u3001\u691c\u5b9a\u3084\u4fe1\u983c\u533a\u9593\u63a8\u5b9a\u306e\u6570\u5024\u3084\u3001R 2 \u4e57\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b<\/p>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u3092\u63cf\u304d\u5165\u308c\u3066\u307f\u308b<\/h2>\n\n\n\n
\u5148\u307b\u3069\u306e\u6563\u5e03\u56f3\u306b\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u3092\u63cf\u304d\u5165\u308c\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\uff23\u5730\u533a\u304c\u5b9f\u7dda\u3067\u3001\uff2f\u5730\u533a\u304c\u70b9\u7dda\uff08lty=2\uff09\u3060\u3002<\/p>\n\n\n\n
abline<\/span>(<\/span>a=<\/span>linreg.c[<\/span>6<\/span>],<\/span> b=<\/span>linreg.c[<\/span>1<\/span>])<\/span>\nabline<\/span>(<\/span>a=<\/span>linreg.o[<\/span>6<\/span>],<\/span> b=<\/span>linreg.o[<\/span>1<\/span>],<\/span> lty=<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u63cf\u304d\u5165\u308c\u305f\u56f3\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\uff08\u50be\u304d\u304c\u540c\u3058\u304b\u3069\u3046\u304b\uff09<\/h2>\n\n\n\n
\u4e0a\u306e\u56f3\u3092\u898b\u308b\u3068\u3001\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u306e\u50be\u304d\u306f\u3068\u3066\u3082\u8fd1\u3044\u304c\u3001\u540c\u3058\u306b\u3057\u3066\u8a71\u3092\u9032\u3081\u3066\u3082\u3044\u3044\u304b\u3069\u3046\u304b\u306e\u691c\u5b9a\u3002<\/p>\n\n\n\n
R\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
reg.line.diff <-<\/span> function<\/span>(<\/span>X1,<\/span> Y1,<\/span> X2,<\/span> Y2){<\/span>\nX <-<\/span> c<\/span>(<\/span>X1,<\/span>X2)<\/span>\nY <-<\/span> c<\/span>(<\/span>Y1,<\/span>Y2)<\/span>\nX1bar <-<\/span> mean<\/span>(<\/span>X1)<\/span>\nX2bar <-<\/span> mean<\/span>(<\/span>X2)<\/span>\nXbar  <-<\/span> mean<\/span>(<\/span>X)<\/span>\nY1bar <-<\/span> mean<\/span>(<\/span>Y1)<\/span>\nY2bar <-<\/span> mean<\/span>(<\/span>Y2)<\/span>\nYbar  <-<\/span> mean<\/span>(<\/span>Y)<\/span>\nSSXY1 <-<\/span> sum<\/span>((<\/span>X1-<\/span>X1bar)<\/span>*<\/span>(<\/span>Y1-<\/span>Y1bar))<\/span>\nSSXY2 <-<\/span> sum<\/span>((<\/span>X2-<\/span>X2bar)<\/span>*<\/span>(<\/span>Y2-<\/span>Y2bar))<\/span>\nSSXY  <-<\/span> sum<\/span>((<\/span>X-<\/span>Xbar)<\/span>*<\/span>(<\/span>Y-<\/span>Ybar))<\/span>\nSSX1  <-<\/span> sum<\/span>((<\/span>X1-<\/span>X1bar)<\/span>^<\/span>2<\/span>)<\/span>\nSSX2  <-<\/span> sum<\/span>((<\/span>X2-<\/span>X2bar)<\/span>^<\/span>2<\/span>)<\/span>\nSSX   <-<\/span> sum<\/span>((<\/span>X-<\/span>Xbar)<\/span>^<\/span>2<\/span>)<\/span>\nSSY1  <-<\/span> sum<\/span>((<\/span>Y1-<\/span>Y1bar)<\/span>^<\/span>2<\/span>)<\/span>\nSSY2  <-<\/span> sum<\/span>((<\/span>Y2-<\/span>Y2bar)<\/span>^<\/span>2<\/span>)<\/span>\nSSY   <-<\/span> sum<\/span>((<\/span>Y-<\/span>Ybar)<\/span>^<\/span>2<\/span>)<\/span>\nDelta1 <-<\/span> SSY1-<\/span>(<\/span>SSXY1)<\/span>^<\/span>2<\/span>\/<\/span>SSX1 +<\/span> SSY2-<\/span>(<\/span>SSXY2)<\/span>^<\/span>2<\/span>\/<\/span>SSX2\nDelta2 <-<\/span> SSY1+<\/span>SSY2 -<\/span> (<\/span>SSXY1+<\/span>SSXY2)<\/span>^<\/span>2<\/span>\/<\/span>(<\/span>SSX1+<\/span>SSX2)<\/span>\nn <-<\/span> length<\/span>(<\/span>X1)<\/span>\nm <-<\/span> length<\/span>(<\/span>X2)<\/span>\nN  <-<\/span> n+<\/span>m\nFb <-<\/span> (<\/span>Delta2-<\/span>Delta1)<\/span>\/<\/span>(<\/span>Delta1\/<\/span>(<\/span>N-<\/span>4<\/span>))<\/span>\npb <-<\/span> pf<\/span>(<\/span>Fb,<\/span> 1<\/span>,<\/span> N-<\/span>4<\/span>,<\/span> lower.tail=<\/span>F<\/span>)<\/span>\nb1 <-<\/span> SSXY1\/<\/span>SSX1\nb2 <-<\/span> SSXY2\/<\/span>SSX2\na1 <-<\/span> Y1bar-<\/span>b1*<\/span>X1bar\na2 <-<\/span> Y2bar-<\/span>b2*<\/span>X2bar\nbE <-<\/span> (<\/span>SSXY1+<\/span>SSXY2)<\/span>\/<\/span>(<\/span>SSX1+<\/span>SSX2)<\/span>\nDelta3 <-<\/span> SSY-<\/span>(<\/span>SSXY)<\/span>^<\/span>2<\/span>\/<\/span>SSX\nFa <-<\/span> (<\/span>Delta3-<\/span>Delta2)<\/span>\/<\/span>(<\/span>Delta2\/<\/span>(<\/span>N-<\/span>3<\/span>))<\/span>\npa <-<\/span> pf<\/span>(<\/span>Fa,<\/span> 1<\/span>,<\/span> N-<\/span>3<\/span>,<\/span> lower.tail=<\/span>F<\/span>)<\/span>\naE1 <-<\/span> Y1bar-<\/span>bE*<\/span>X1bar\naE2 <-<\/span> Y2bar-<\/span>bE*<\/span>X2bar\nbT <-<\/span> SSXY\/<\/span>SSX\naT <-<\/span> Ybar-<\/span>bT*<\/span>Xbar\na.diff <-<\/span> aE2-<\/span>aE1\na.diff.l <-<\/span> a.diff-<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> N-<\/span>3<\/span>)<\/span>*<\/span>sqrt<\/span>((<\/span>1<\/span>\/<\/span>n+<\/span>1<\/span>\/<\/span>m+<\/span>(<\/span>X1bar-<\/span>X2bar)<\/span>^<\/span>2<\/span>\/<\/span>(<\/span>SSX1+<\/span>SSX2))<\/span>*<\/span>(<\/span>Delta2\/<\/span>(<\/span>N-<\/span>3<\/span>)))<\/span>\na.diff.u <-<\/span> a.diff+<\/span>qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> N-<\/span>3<\/span>)<\/span>*<\/span>sqrt<\/span>((<\/span>1<\/span>\/<\/span>n+<\/span>1<\/span>\/<\/span>m+<\/span>(<\/span>X1bar-<\/span>X2bar)<\/span>^<\/span>2<\/span>\/<\/span>(<\/span>SSX1+<\/span>SSX2))<\/span>*<\/span>(<\/span>Delta2\/<\/span>(<\/span>N-<\/span>3<\/span>)))<\/span>\nconf <-<\/span> qt<\/span>(<\/span>1<\/span>-<\/span>0.05<\/span>\/<\/span>2<\/span>,<\/span> N-<\/span>3<\/span>)<\/span>*<\/span>sqrt<\/span>((<\/span>1<\/span>\/<\/span>n+<\/span>1<\/span>\/<\/span>m+<\/span>(<\/span>X1bar-<\/span>X2bar)<\/span>^<\/span>2<\/span>\/<\/span>(<\/span>SSX1+<\/span>SSX2))<\/span>*<\/span>(<\/span>Delta2\/<\/span>(<\/span>N-<\/span>3<\/span>)))<\/span>\nlist<\/span>(<\/span>c<\/span>(<\/span>Delta1=<\/span>Delta1,<\/span> Delta2=<\/span>Delta2,<\/span> F_Slopes=<\/span>Fb,<\/span> p_Slopes=<\/span>pb,<\/span>\nDelta3=<\/span>Delta3,<\/span> F_Intcps=<\/span>Fa,<\/span> p_Intcps=<\/span>pa,<\/span>\nSlope1=<\/span>b1,<\/span> Slope2=<\/span>b2,<\/span> Intcp1=<\/span>a1,<\/span> Intcp2=<\/span>a2,<\/span>\nSlope_Common=<\/span>bE,<\/span> Intcp1_Slope_Common=<\/span>aE1,<\/span> Intcp2_Slope_Common=<\/span>aE2,<\/span>\nDiff_Intcps=<\/span>a.diff,<\/span> Diff_Intcps_LL=<\/span>a.diff.l,<\/span> Diff_Intcps_UL=<\/span>a.diff.u,<\/span>\nSlop_Total=<\/span>bT,<\/span> Intcp_Total=<\/span>aT))<\/span>\n}<\/span>\nreg.line.diff1 <-<\/span> unlist<\/span>(<\/span>reg.line.diff<\/span>(<\/span>X1=<\/span>NO2.c,<\/span> Y1=<\/span>pre.c,<\/span> X2=<\/span>NO2.o,<\/span> Y2=<\/span>pre.o))<\/span>\nreg.line.diff1\n<\/code><\/pre>\n\n\n\n
\u30b9\u30af\u30ea\u30d7\u30c8\u5185\u3067\u3001\u30ca\u30f3\u30c8\u30abbar\u306f\u5e73\u5747\u3001SS\u30ca\u30f3\u30c8\u30ab\u306f\u5e73\u65b9\u548c\uff08\u5e73\u5747\u3068\u306e\u5dee\u306e\u4e8c\u4e57\u548c\uff09\u3084\u7a4d\u548c\uff08X\u306e\u5e73\u5747\u3068\u306e\u5dee\u3068Y\u306e\u5e73\u5747\u3068\u306e\u5dee\u306e\u7a4d\u306e\u548c\uff09\u3002<\/p>\n\n\n\n
\u305d\u308c\u3089\u3092\u4f7f\u3063\u3066\u3001Delta1, Delta2, Delta3\u3092\u8a08\u7b97\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
Delta1\u306f\u3001\u50be\u304d\u304c\u7570\u306a\u308b\u3068\u3044\u3046\u4eee\u8aac\uff08\u5bfe\u7acb\u4eee\u8aac\uff09\u306e\u3082\u3068\u3067\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u3002<\/p>\n\n\n\n
Delta2\u306f\u3001\u50be\u304d\u306f\u7b49\u3057\u3044\u3068\u3044\u3046\u4eee\u8aac\uff08\u5e30\u7121\u4eee\u8aac\uff09\u306e\u3082\u3068\u3067\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u3002<\/p>\n\n\n\n
Delta3\u306f\u3001\u50be\u304d\u3082\u5207\u7247\u3082\u7b49\u3057\u3044\u3068\u3044\u3046\u4eee\u8aac\u306e\u4e0b\u3067\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u3002<\/p>\n\n\n\n
\u50be\u304d\u306e\u691c\u5b9a\u306fDelta1\u3068Delta2\u3092\u4f7f\u3063\u3066F\u5206\u5e03\u3067\u691c\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n
F\u5024\u306e\u5206\u5b50\u306e\u81ea\u7531\u5ea6\u306f\u5730\u533a\u306e\u6570\uff082\uff09\u30de\u30a4\u30ca\u30b9 1=1\u3001\u5206\u6bcd\u306e\u81ea\u7531\u5ea6\u306f\u3001\u5168\u4f53\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff08N\uff09\u30de\u30a4\u30ca\u30b9 \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570\uff084\u3064\uff09\u3002<\/p>\n\n\n\n
4\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u306f\u3001Intercept\u3001Slope\u3001\u5730\u533a\u3001Slope\u3068\u5730\u533a\u306e\u4ea4\u4e92\u4f5c\u7528\uff08\u5730\u533a\u3054\u3068\u306bSlope\u304c\u7570\u306a\u308b\u3068\u3044\u3046\u4eee\u8aac\uff09\u306e4\u3064\u3002<\/p>\n\n\n\n
\u5207\u7247\u306e\u691c\u5b9a\u306f\u3001Delta2\u3068Delta3\u3092\u4f7f\u3063\u3066F\u5206\u5e03\u3067\u691c\u5b9a\u3002<\/p>\n\n\n\n
F\u5024\u306e\u5206\u5b50\u306e\u81ea\u7531\u5ea6\u306f\u5148\u307b\u3069\u3068\u540c\u3058\u304f\u5730\u533a\u306e\u6570\uff082\uff09\u30de\u30a4\u30ca\u30b9 1=1\u3001\u5206\u6bcd\u306e\u81ea\u7531\u5ea6\u306f\u3001N \u30de\u30a4\u30ca\u30b9 \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570\uff083\uff09\u3002<\/p>\n\n\n\n
3\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3001Intercept\u3001Slope\u3001\u5730\u533a\u306e3\u3064\u3002<\/p>\n\n\n\n
\u7d50\u679c\u306f\u3001\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> reg.line.diff1\nDelta1              Delta2            F_Slopes\n64.754442586<\/span>        65.052361246<\/span>         0.078212660<\/span>\np_Slopes              Delta3            F_Intcps\n0.783108529<\/span>        96.837793841<\/span>         8.795034888<\/span>\np_Intcps              Slope1              Slope2\n0.008280926<\/span>       279.854182655<\/span>       317.540322581<\/span>\nIntcp1              Intcp2        Slope_Common\n-<\/span>1.489293937<\/span>         0.110080645<\/span>       290.976955534<\/span>\nIntcp1_Slope_Common Intcp2_Slope_Common         Diff_Intcps\n-<\/span>1.751184680<\/span>         0.715725414<\/span>         2.466910094<\/span>\nDiff_Intcps_LL      Diff_Intcps_UL          Slop_Total\n0.719300276<\/span>         4.214519912<\/span>       281.451309098<\/span>\nIntcp_Total\n-<\/span>0.355561311<\/span>\n<\/code><\/pre>\n\n\n\n
\u50be\u304d\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u306a\u304b\u3063\u305f\uff08p_Slopes \u2252 0.78\uff09\u306e\u3067\u3001\u540c\u3058\u50be\u304d\u306b\u3057\u3066\u8a71\u3092\u9032\u3081\u3066\u3082\u3088\u3044\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u5171\u901a\u306e\u50be\u304d\u306f Slope_Common \u2252 290.98 \u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u50be\u304d\u304c\u7b49\u3057\u3044\u4e0a\u3067\u3001\u5207\u7247\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u305f\uff08p_Intcps \u2252 0.0083\uff09\u306e\u3067\u3001\u5207\u7247\u306f\u7570\u306a\u3063\u3066\u3001C\u5730\u533a\u3068O\u5730\u533a\u306e\u56de\u5e30\u76f4\u7dda\u306f\u4e26\u884c\u3060\u304c\u5225\u3005\u304c\u3088\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
\u5207\u7247\u306e\u5dee\u306f Diff_Intcps \u2252 2.47 \u3067\u7d042.5%\u3060\u3002<\/p>\n\n\n\n
95%\u4fe1\u983c\u533a\u9593\u306f0.72\uff05\u304b\u30894.2\uff05\uff08Diff_Intcps_LL \u2252 0.72, Diff_Intcps_UL \u2252 4.21\uff09\u3002<\/p>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u306e\u50be\u304d\u304c\u5171\u901a\u3067\u5207\u7247\u304c\u7570\u306a\u308b\u3068\u3044\u3046\u7d50\u679c\u3092\u56de\u5e30\u76f4\u7dda\u306b\u3057\u3066\u63cf\u304d\u5165\u308c\u3066\u307f\u308b<\/h2>\n\n\n\n
\u7d50\u679c\u3092\u56f3\u306b\u63cf\u304d\u5165\u308c\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u5171\u901a\u306e\u50be\u304d\u306e\u7dda\u306f\u8d64\uff08col=2\uff09\u3067\u8868\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
C\u5730\u533a\u306f\u5b9f\u7dda\u3067\u3001O\u5730\u533a\u306f\u70b9\u7dda\u3060\u3002\u5225\u3005\u306e\u56de\u5e30\u76f4\u7dda\uff08\u9ed2\uff09\u3068\u307b\u3068\u3093\u3069\u9055\u308f\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u305d\u308c\u306a\u3089\u3070\u30b7\u30f3\u30d7\u30eb\u306a\u307b\u3046\u304c\u3044\u3044\u3002<\/p>\n\n\n\n
\u3064\u307e\u308a\u3001NO2\u6fc3\u5ea6\u3068\u6709\u75c7\u5272\u5408\u306e\u95a2\u4fc2\u306f\u5730\u533a\u306b\u3088\u3063\u3066\u7570\u306a\u3089\u306a\u3044\u304c\u3001\u5404\u5730\u533a\u3067\u306e\u6709\u75c7\u5272\u5408\u30ec\u30d9\u30eb\u304c\u9ad8\u3044\u304b\u4f4e\u3044\u304b\u306e\u9055\u3044\u304c\u3042\u308b\u3068\u3044\u3046\u30b7\u30f3\u30d7\u30eb\u306a\u307b\u3046\u304c\u3044\u3044\u3002<\/p>\n\n\n\n
\u30b7\u30f3\u30d7\u30eb\u306a\u307b\u3046\u304c\u3001\u307b\u304b\u306e\u5730\u533a\u306b\u3082\u5fdc\u7528\u304c\u5229\u304f\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3002<\/p>\n\n\n\n
abline<\/span>(<\/span>a=<\/span>reg.line.diff1[<\/span>13<\/span>],<\/span> b=<\/span>reg.line.diff1[<\/span>12<\/span>],<\/span> col=<\/span>2<\/span>)<\/span>\nabline<\/span>(<\/span>a=<\/span>reg.line.diff1[<\/span>14<\/span>],<\/span> b=<\/span>reg.line.diff1[<\/span>12<\/span>],<\/span> col=<\/span>2<\/span>,<\/span> lty=<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\u3092 lm() \u3067\u5b9f\u65bd\u3057\u3066\u307f\u308b\u3068\u3069\u3046\u306a\u308b\u304b<\/h2>\n\n\n\n
\u7d71\u8a08\u30bd\u30d5\u30c8R\u306b\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u308b\u95a2\u6570 lm() \u3092\u4f7f\u3046\u3068\u3069\u3093\u306a\u3075\u3046\u306b\u3067\u304d\u308b\u304b\u898b\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u307e\u305a\u30c7\u30fc\u30bf\u3092\u5c11\u3057\u52a0\u5de5\u3059\u308b<\/h3>\n\n\n\n
dat <-<\/span> data.frame<\/span>(<\/span>NO2=<\/span>c<\/span>(<\/span>NO2.c,<\/span>NO2.o),<\/span>pre=<\/span>c<\/span>(<\/span>pre.c,<\/span>pre.o),<\/span>are=<\/span>c<\/span>(<\/span>are.c,<\/span>are.o))<\/span>\n<\/code><\/pre>\n\n\n\n
\u4ea4\u4e92\u4f5c\u7528\u9805\u3092\u5165\u308c\u305f\u30e2\u30c7\u30eb\uff08\u50be\u304d\u304c\u5225\u3005\u306e\u30e2\u30c7\u30eb\uff09<\/h3>\n\n\n\n
\u4e0a\u8a18\u3067Delta1\u3092\u8a08\u7b97\u3057\u305f\u306e\u3068\u540c\u7b49\u306a\u306e\u304c\u3001\u4ea4\u4e92\u4f5c\u7528\u9805\u3092\u5165\u308c\u305f\u30e2\u30c7\u30eb\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
lm1 <-<\/span> lm<\/span>(<\/span>pre~<\/span>NO2*<\/span>are,<\/span> data=<\/span>dat)<\/span>\nlibrary<\/span>(<\/span>car)<\/span>\nAnova<\/span>(<\/span>lm1)<\/span>\n<\/code><\/pre>\n\n\n\n
Anova()\u3092\u4f7f\u3046\u306e\u3067car \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u3066\u3001\u4f7f\u3048\u308b\u3088\u3046\u306b\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u306b\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\tR\u306f\u3001\u6700\u521d\u304b\u3089\u304b\u306a\u308a\u3044\u308d\u3044\u308d\u306a\u3053\u3068\u304c\u3067\u304d\u308b\u7121\u6599\u7d71\u8a08\u30bd\u30d5\u30c8\u3002 \u3082\u3063\u3068\u3059\u3054\u3044\u306e\u306f\u3001\u3042\u3068\u304b\u3089\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u3066\u3001\u3055\u3089\u306b\u3044\u308d\u3044\u308d\u306a\u89e3\u6790\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n
><\/span> Anova<\/span>(<\/span>lm1)<\/span>\nAnova Table <\/span>(<\/span>Type II tests)<\/span>\nResponse:<\/span> pre\nSum Sq Df F<\/span> value    Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\nNO2       85.373<\/span>  1<\/span> 22.4129<\/span> 0.0001918<\/span> ***<\/span>\nare       31.785<\/span>  1<\/span>  8.3446<\/span> 0.0102038<\/span> *<\/span>\nNO2:<\/span>are    0.298<\/span>  1<\/span>  0.0782<\/span> 0.7831085<\/span>\nResiduals 64.754<\/span> 17<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n<\/code><\/pre>\n\n\n\n
NO2:are \u304c\u4ea4\u4e92\u4f5c\u7528\u9805\u3002<\/p>\n\n\n\n
p\u5024\u306f0.7831085\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u4e0a\u8a18\u306e\u50be\u304d\u304c\u7b49\u3057\u3044\u5e30\u7121\u4eee\u8aac\u306e\u691c\u5b9a\uff08p_Slopes=0.783108529\uff09\u3068\u7d50\u679c\u304c\u540c\u3058\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
Residuals\u306fDelta1\u306b\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n
\u4ea4\u4e92\u4f5c\u7528\u304c\u6709\u610f\u3067\u306a\u3044\u306e\u3067\u4ea4\u4e92\u4f5c\u7528\u9805\u3092\u5165\u308c\u306a\u3044\u30e2\u30c7\u30eb\u306b\u3059\u308b<\/h3>\n\n\n\n
\u3053\u306e\u30e2\u30c7\u30eb\u304c\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u306e\u50be\u304d\u304c\u540c\u3058\u3068\u8003\u3048\u305f\u5834\u5408\u306b\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n
\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ea4\u4e92\u4f5c\u7528\u3092\u5916\u3057\u305f\u30b7\u30f3\u30d7\u30eb\u306a\u3082\u306e\u3060\u3002<\/p>\n\n\n\n
lm2 <-<\/span> lm<\/span>(<\/span>pre~<\/span>NO2+<\/span>are,<\/span> data=<\/span>dat)<\/span>\nsummary<\/span>(<\/span>lm2)<\/span>\nconfint<\/span>(<\/span>lm2)<\/span>\nAnova<\/span>(<\/span>lm2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>lm2)<\/span>\nCall:<\/span>\nlm<\/span>(<\/span>formula =<\/span> pre ~<\/span> NO2 +<\/span> are,<\/span> data =<\/span> dat)<\/span>\nResiduals:<\/span>\nMin      1Q  Median      3Q     Max\n-<\/span>3.4781<\/span> -<\/span>1.3413<\/span> -<\/span>0.1781<\/span>  0.9595<\/span>  5.1038<\/span>\nCoefficients:<\/span>\nEstimate Std. Error t value Pr<\/span>(<\/span>>|<\/span>t|<\/span>)<\/span>\n(<\/span>Intercept)<\/span>  -<\/span>1.7512<\/span>     1.5217<\/span>  -<\/span>1.151<\/span> 0.264870<\/span>\nNO2         290.9770<\/span>    59.8680<\/span>   4.860<\/span> 0.000126<\/span> ***<\/span>\nareo          2.4669<\/span>     0.8318<\/span>   2.966<\/span> 0.008281<\/span> **<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\nResidual standard error:<\/span> 1.901<\/span> on 18<\/span> degrees of freedom\nMultiple R-<\/span>squared:<\/span>  0.6324<\/span>,<\/span>    Adjusted R-<\/span>squared:<\/span>  0.5915<\/span>\nF<\/span>-<\/span>statistic:<\/span> 15.48<\/span> on 2<\/span> and 18<\/span> DF,<\/span>  p-<\/span>value:<\/span> 0.0001227<\/span>\n<\/code><\/pre>\n\n\n\n
NO2\u306eEstimate\u304c\u3001\u4e0a\u8a18\u3067\u5171\u901a\u306e\u50be\u304d\u3068\u79f0\u3057\u305f\u5024\uff08Slope_Common=290.976955534\uff09\u306b\u4e00\u81f4\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001areo\u306eEstimate\u304c\u4e0a\u8a18\u3067\u8a00\u3063\u3066\u3044\u305f\u5207\u7247\u306e\u5dee\uff08Diff_Intcps=2.466910094\uff09\u306b\u4e00\u81f4\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
Intercept\u306eEstimate\u3068\u8db3\u3057\u5408\u308f\u305b\u308b\u3068\u3001O\u5730\u533a\u306e\u5207\u7247\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
Intercept\u306eEstimate\u306fC\u5730\u533a\u306e\u5207\u7247\uff08Intcp1_Slope_Common=-1.751184680\uff09\u3068\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n
95\uff05\u4fe1\u983c\u533a\u9593\u306e\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> confint<\/span>(<\/span>lm2)<\/span>\n2.5<\/span> %     97.5<\/span> %\n(<\/span>Intercept)<\/span>  -<\/span>4.9481583<\/span>   1.445789<\/span>\nNO2         165.1990206<\/span> 416.754891<\/span>\nareo          0.7193003<\/span>   4.214520<\/span>\n<\/code><\/pre>\n\n\n\n
areo\u306e95%\u4fe1\u983c\u533a\u9593\u306f\u3001\u5207\u7247\u306e\u5dee\u306e\u4fe1\u983c\u533a\u9593\uff08Diff_Intcps_LL=0.719300276, Diff_Intcps_UL=4.214519912\uff09\u306b\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n
\u3053\u306e\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u304cDelta2=65.052361246\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
><\/span> Anova<\/span>(<\/span>lm2)<\/span>\nAnova Table <\/span>(<\/span>Type II tests)<\/span>\nResponse:<\/span> pre\nSum Sq Df F<\/span> value    Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\nNO2       85.373<\/span>  1<\/span>  23.623<\/span> 0.0001257<\/span> ***<\/span>\nare       31.785<\/span>  1<\/span>   8.795<\/span> 0.0082809<\/span> **<\/span>\nResiduals 65.052<\/span> 18<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n<\/code><\/pre>\n\n\n\n
\u3082\u3057\u5730\u57df\u5dee\u304c\u306a\u3051\u308c\u3070\u5730\u57df\u306e\u8981\u56e0\u3082\u53d6\u308a\u9664\u3044\u3066\u5207\u7247\u3082\u540c\u3058\u3068\u8003\u3048\u3066\u3082\u3088\u3044<\/h3>\n\n\n\n
\u5730\u57df\u3067\u6709\u610f\u306b\u7570\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3053\u3053\u3067\u7d42\u4e86\u3060\u304c\u3001\u3082\u3057\u5730\u57df\u5dee\u3082\u306a\u3044\u3001\u3064\u307e\u308a\u5207\u7247\u3082\u7570\u306a\u3089\u306a\u3044\u306e\u3067\u3042\u308c\u3070\u3001\u5b8c\u5168\u306b\u4e00\u3064\u306e\u56de\u5e30\u76f4\u7dda\u306b\u3057\u3066\u3057\u307e\u3063\u3066\u3082\u3088\u3044\u3002<\/p>\n\n\n\n
lm3 <-<\/span> lm<\/span>(<\/span>pre~<\/span>NO2,<\/span> data=<\/span>dat)<\/span>\nAnova<\/span>(<\/span>lm3)<\/span>\n<\/code><\/pre>\n\n\n\n
\u3053\u306e\u6642\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u304cDelta3=96.837793841\u306a\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
><\/span> Anova<\/span>(<\/span>lm3)<\/span>\nAnova Table <\/span>(<\/span>Type II tests)<\/span>\nResponse:<\/span> pre\nSum Sq Df F<\/span> value   Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\nNO2       80.105<\/span>  1<\/span>  15.717<\/span> 0.000831<\/span> ***<\/span>\nResiduals 96.838<\/span> 19<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a\u3092\u5f15\u7528\u66f8\u7c4d\u306b\u6cbf\u3063\u3066\u78ba\u8a8d\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
\u50be\u304d\u304c\u7570\u306a\u308b\u304b\u3069\u3046\u304b\u306f\u4ea4\u4e92\u4f5c\u7528\u9805\u3092 lm() \u5185\u306b\u6295\u5165\u3059\u308c\u3070\u3088\u3044\u304c\u3001lm()\u3092\u4f7f\u308f\u306a\u3044\u5834\u5408\u306f\u3069\u3046\u3084\u308b\u304b\u3001\u3069\u3093\u306a\u6b8b\u5dee\u5e73\u65b9\u548c\u3092\u4f7f\u3063\u3066\u691c\u5b9a\u3059\u308b\u306e\u304b\u304c\u8a73\u7d30\u306b\u78ba\u8a8d\u3067\u304d\u305f\u3002<\/p>\n\n\n\n
\u4e8c\u3064\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u3042\u3063\u3066\u3001\u4e8c\u3064\u306e\u56de\u5e30\u76f4\u7dda\u304c\u5f15\u3051\u305f\u304c\u3001\u3055\u3066\u3053\u306e\u5f8c\u3069\u3046\u3059\u308b\u304b\uff1f\u3068\u60a9\u3093\u3067\u3057\u307e\u3063\u3066\u3044\u308b\u4eba\u306e\u6b21\u306e\u4e00\u624b\u306b\u306a\u308b\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
\u5f15\u7528\u66f8\u7c4d<\/h2>\n\n\n\n
\u30cd\u30bf\u672c\u306f\u300c\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66\u300d6.2.3 \u4e8c\u3064\u306e\u6bcd\u56de\u5e30\u76f4\u7dda\u306e\u5dee\u306e\u691c\u5b9a<\/p>\n\n\n\n
\"\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66<\/a><\/figure>\n\n\n\n
<\/div>\n\n\n\n
\n
\u533b\u5b66\u3078\u306e\u7d71\u8a08\u5b66 (\u7d71\u8a08\u30e9\u30a4\u30d6\u30e9\u30ea\u30fc)<\/a><\/p>\n