slr<-read.csv("E:\\Data science\\Practies\\Linear Regression.csv")
View(slr)
dim(slr)
## [1] 300 2
attach(slr)
mean(X)
## [1] 150.5
mean(Y)
## [1] 102.2156
median(X)
## [1] 150.5
median(Y)
## [1] 102.2222
sd(X)
## [1] 86.74676
sd(Y)
## [1] 57.84271
var(X)
## [1] 7525
var(Y)
## [1] 3345.779
library(moments)
skewness(X)
## [1] 0
skewness(Y)
## [1] -0.0006876861
kurtosis(slr)
## X Y
## 1.799973 1.800919
hist(X)
hist(Y)
barplot(X)
barplot(Y)
boxplot(X)
boxplot(Y)
cor(X,Y)
## [1] 0.9598758
plot(Y,X)
m1<-lm(Y~X,data=slr)
summary(m1)
##
## Call:
## lm(formula = Y ~ X, data = slr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -196.013 -0.703 1.287 3.277 5.267
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.88880 1.88083 3.131 0.00192 **
## X 0.64004 0.01083 59.089 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.25 on 298 degrees of freedom
## Multiple R-squared: 0.9214, Adjusted R-squared: 0.9211
## F-statistic: 3491 on 1 and 298 DF, p-value: < 2.2e-16
m2<-lm(Y~log(X),data=slr)
summary(m2)
##
## Call:
## lm(formula = Y ~ log(X), data = slr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -151.076 -22.748 -5.931 20.004 144.071
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -140.182 8.584 -16.33 <2e-16 ***
## log(X) 51.395 1.783 28.82 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.77 on 298 degrees of freedom
## Multiple R-squared: 0.736, Adjusted R-squared: 0.7351
## F-statistic: 830.8 on 1 and 298 DF, p-value: < 2.2e-16
m3<-lm(log(Y)~X,data=slr)
summary(m3)
##
## Call:
## lm(formula = log(Y) ~ X, data = slr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9573 -0.0944 0.1287 0.2690 0.3176
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.1119592 0.0611889 50.86 <2e-16 ***
## X 0.0082710 0.0003524 23.47 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5286 on 298 degrees of freedom
## Multiple R-squared: 0.6489, Adjusted R-squared: 0.6478
## F-statistic: 550.9 on 1 and 298 DF, p-value: < 2.2e-16
pv<-predict(m1)
pv
## 1 2 3 4 5 6
## 6.528845 7.168889 7.808934 8.448979 9.089024 9.729069
## 7 8 9 10 11 12
## 10.369114 11.009159 11.649204 12.289249 12.929293 13.569338
## 13 14 15 16 17 18
## 14.209383 14.849428 15.489473 16.129518 16.769563 17.409608
## 19 20 21 22 23 24
## 18.049653 18.689697 19.329742 19.969787 20.609832 21.249877
## 25 26 27 28 29 30
## 21.889922 22.529967 23.170012 23.810057 24.450101 25.090146
## 31 32 33 34 35 36
## 25.730191 26.370236 27.010281 27.650326 28.290371 28.930416
## 37 38 39 40 41 42
## 29.570461 30.210506 30.850550 31.490595 32.130640 32.770685
## 43 44 45 46 47 48
## 33.410730 34.050775 34.690820 35.330865 35.970910 36.610954
## 49 50 51 52 53 54
## 37.250999 37.891044 38.531089 39.171134 39.811179 40.451224
## 55 56 57 58 59 60
## 41.091269 41.731314 42.371358 43.011403 43.651448 44.291493
## 61 62 63 64 65 66
## 44.931538 45.571583 46.211628 46.851673 47.491718 48.131762
## 67 68 69 70 71 72
## 48.771807 49.411852 50.051897 50.691942 51.331987 51.972032
## 73 74 75 76 77 78
## 52.612077 53.252122 53.892166 54.532211 55.172256 55.812301
## 79 80 81 82 83 84
## 56.452346 57.092391 57.732436 58.372481 59.012526 59.652570
## 85 86 87 88 89 90
## 60.292615 60.932660 61.572705 62.212750 62.852795 63.492840
## 91 92 93 94 95 96
## 64.132885 64.772930 65.412974 66.053019 66.693064 67.333109
## 97 98 99 100 101 102
## 67.973154 68.613199 69.253244 69.893289 70.533334 71.173378
## 103 104 105 106 107 108
## 71.813423 72.453468 73.093513 73.733558 74.373603 75.013648
## 109 110 111 112 113 114
## 75.653693 76.293738 76.933782 77.573827 78.213872 78.853917
## 115 116 117 118 119 120
## 79.493962 80.134007 80.774052 81.414097 82.054142 82.694186
## 121 122 123 124 125 126
## 83.334231 83.974276 84.614321 85.254366 85.894411 86.534456
## 127 128 129 130 131 132
## 87.174501 87.814546 88.454590 89.094635 89.734680 90.374725
## 133 134 135 136 137 138
## 91.014770 91.654815 92.294860 92.934905 93.574950 94.214994
## 139 140 141 142 143 144
## 94.855039 95.495084 96.135129 96.775174 97.415219 98.055264
## 145 146 147 148 149 150
## 98.695309 99.335354 99.975398 100.615443 101.255488 101.895533
## 151 152 153 154 155 156
## 102.535578 103.175623 103.815668 104.455713 105.095758 105.735802
## 157 158 159 160 161 162
## 106.375847 107.015892 107.655937 108.295982 108.936027 109.576072
## 163 164 165 166 167 168
## 110.216117 110.856162 111.496206 112.136251 112.776296 113.416341
## 169 170 171 172 173 174
## 114.056386 114.696431 115.336476 115.976521 116.616566 117.256610
## 175 176 177 178 179 180
## 117.896655 118.536700 119.176745 119.816790 120.456835 121.096880
## 181 182 183 184 185 186
## 121.736925 122.376970 123.017014 123.657059 124.297104 124.937149
## 187 188 189 190 191 192
## 125.577194 126.217239 126.857284 127.497329 128.137374 128.777418
## 193 194 195 196 197 198
## 129.417463 130.057508 130.697553 131.337598 131.977643 132.617688
## 199 200 201 202 203 204
## 133.257733 133.897778 134.537822 135.177867 135.817912 136.457957
## 205 206 207 208 209 210
## 137.098002 137.738047 138.378092 139.018137 139.658182 140.298226
## 211 212 213 214 215 216
## 140.938271 141.578316 142.218361 142.858406 143.498451 144.138496
## 217 218 219 220 221 222
## 144.778541 145.418586 146.058630 146.698675 147.338720 147.978765
## 223 224 225 226 227 228
## 148.618810 149.258855 149.898900 150.538945 151.178990 151.819034
## 229 230 231 232 233 234
## 152.459079 153.099124 153.739169 154.379214 155.019259 155.659304
## 235 236 237 238 239 240
## 156.299349 156.939394 157.579438 158.219483 158.859528 159.499573
## 241 242 243 244 245 246
## 160.139618 160.779663 161.419708 162.059753 162.699798 163.339843
## 247 248 249 250 251 252
## 163.979887 164.619932 165.259977 165.900022 166.540067 167.180112
## 253 254 255 256 257 258
## 167.820157 168.460202 169.100247 169.740291 170.380336 171.020381
## 259 260 261 262 263 264
## 171.660426 172.300471 172.940516 173.580561 174.220606 174.860651
## 265 266 267 268 269 270
## 175.500695 176.140740 176.780785 177.420830 178.060875 178.700920
## 271 272 273 274 275 276
## 179.340965 179.981010 180.621055 181.261099 181.901144 182.541189
## 277 278 279 280 281 282
## 183.181234 183.821279 184.461324 185.101369 185.741414 186.381459
## 283 284 285 286 287 288
## 187.021503 187.661548 188.301593 188.941638 189.581683 190.221728
## 289 290 291 292 293 294
## 190.861773 191.501818 192.141863 192.781907 193.421952 194.061997
## 295 296 297 298 299 300
## 194.702042 195.342087 195.982132 196.622177 197.262222 197.902267
pv1<-as.data.frame(pv)
pv1
## pv
## 1 6.528845
## 2 7.168889
## 3 7.808934
## 4 8.448979
## 5 9.089024
## 6 9.729069
## 7 10.369114
## 8 11.009159
## 9 11.649204
## 10 12.289249
## 11 12.929293
## 12 13.569338
## 13 14.209383
## 14 14.849428
## 15 15.489473
## 16 16.129518
## 17 16.769563
## 18 17.409608
## 19 18.049653
## 20 18.689697
## 21 19.329742
## 22 19.969787
## 23 20.609832
## 24 21.249877
## 25 21.889922
## 26 22.529967
## 27 23.170012
## 28 23.810057
## 29 24.450101
## 30 25.090146
## 31 25.730191
## 32 26.370236
## 33 27.010281
## 34 27.650326
## 35 28.290371
## 36 28.930416
## 37 29.570461
## 38 30.210506
## 39 30.850550
## 40 31.490595
## 41 32.130640
## 42 32.770685
## 43 33.410730
## 44 34.050775
## 45 34.690820
## 46 35.330865
## 47 35.970910
## 48 36.610954
## 49 37.250999
## 50 37.891044
## 51 38.531089
## 52 39.171134
## 53 39.811179
## 54 40.451224
## 55 41.091269
## 56 41.731314
## 57 42.371358
## 58 43.011403
## 59 43.651448
## 60 44.291493
## 61 44.931538
## 62 45.571583
## 63 46.211628
## 64 46.851673
## 65 47.491718
## 66 48.131762
## 67 48.771807
## 68 49.411852
## 69 50.051897
## 70 50.691942
## 71 51.331987
## 72 51.972032
## 73 52.612077
## 74 53.252122
## 75 53.892166
## 76 54.532211
## 77 55.172256
## 78 55.812301
## 79 56.452346
## 80 57.092391
## 81 57.732436
## 82 58.372481
## 83 59.012526
## 84 59.652570
## 85 60.292615
## 86 60.932660
## 87 61.572705
## 88 62.212750
## 89 62.852795
## 90 63.492840
## 91 64.132885
## 92 64.772930
## 93 65.412974
## 94 66.053019
## 95 66.693064
## 96 67.333109
## 97 67.973154
## 98 68.613199
## 99 69.253244
## 100 69.893289
## 101 70.533334
## 102 71.173378
## 103 71.813423
## 104 72.453468
## 105 73.093513
## 106 73.733558
## 107 74.373603
## 108 75.013648
## 109 75.653693
## 110 76.293738
## 111 76.933782
## 112 77.573827
## 113 78.213872
## 114 78.853917
## 115 79.493962
## 116 80.134007
## 117 80.774052
## 118 81.414097
## 119 82.054142
## 120 82.694186
## 121 83.334231
## 122 83.974276
## 123 84.614321
## 124 85.254366
## 125 85.894411
## 126 86.534456
## 127 87.174501
## 128 87.814546
## 129 88.454590
## 130 89.094635
## 131 89.734680
## 132 90.374725
## 133 91.014770
## 134 91.654815
## 135 92.294860
## 136 92.934905
## 137 93.574950
## 138 94.214994
## 139 94.855039
## 140 95.495084
## 141 96.135129
## 142 96.775174
## 143 97.415219
## 144 98.055264
## 145 98.695309
## 146 99.335354
## 147 99.975398
## 148 100.615443
## 149 101.255488
## 150 101.895533
## 151 102.535578
## 152 103.175623
## 153 103.815668
## 154 104.455713
## 155 105.095758
## 156 105.735802
## 157 106.375847
## 158 107.015892
## 159 107.655937
## 160 108.295982
## 161 108.936027
## 162 109.576072
## 163 110.216117
## 164 110.856162
## 165 111.496206
## 166 112.136251
## 167 112.776296
## 168 113.416341
## 169 114.056386
## 170 114.696431
## 171 115.336476
## 172 115.976521
## 173 116.616566
## 174 117.256610
## 175 117.896655
## 176 118.536700
## 177 119.176745
## 178 119.816790
## 179 120.456835
## 180 121.096880
## 181 121.736925
## 182 122.376970
## 183 123.017014
## 184 123.657059
## 185 124.297104
## 186 124.937149
## 187 125.577194
## 188 126.217239
## 189 126.857284
## 190 127.497329
## 191 128.137374
## 192 128.777418
## 193 129.417463
## 194 130.057508
## 195 130.697553
## 196 131.337598
## 197 131.977643
## 198 132.617688
## 199 133.257733
## 200 133.897778
## 201 134.537822
## 202 135.177867
## 203 135.817912
## 204 136.457957
## 205 137.098002
## 206 137.738047
## 207 138.378092
## 208 139.018137
## 209 139.658182
## 210 140.298226
## 211 140.938271
## 212 141.578316
## 213 142.218361
## 214 142.858406
## 215 143.498451
## 216 144.138496
## 217 144.778541
## 218 145.418586
## 219 146.058630
## 220 146.698675
## 221 147.338720
## 222 147.978765
## 223 148.618810
## 224 149.258855
## 225 149.898900
## 226 150.538945
## 227 151.178990
## 228 151.819034
## 229 152.459079
## 230 153.099124
## 231 153.739169
## 232 154.379214
## 233 155.019259
## 234 155.659304
## 235 156.299349
## 236 156.939394
## 237 157.579438
## 238 158.219483
## 239 158.859528
## 240 159.499573
## 241 160.139618
## 242 160.779663
## 243 161.419708
## 244 162.059753
## 245 162.699798
## 246 163.339843
## 247 163.979887
## 248 164.619932
## 249 165.259977
## 250 165.900022
## 251 166.540067
## 252 167.180112
## 253 167.820157
## 254 168.460202
## 255 169.100247
## 256 169.740291
## 257 170.380336
## 258 171.020381
## 259 171.660426
## 260 172.300471
## 261 172.940516
## 262 173.580561
## 263 174.220606
## 264 174.860651
## 265 175.500695
## 266 176.140740
## 267 176.780785
## 268 177.420830
## 269 178.060875
## 270 178.700920
## 271 179.340965
## 272 179.981010
## 273 180.621055
## 274 181.261099
## 275 181.901144
## 276 182.541189
## 277 183.181234
## 278 183.821279
## 279 184.461324
## 280 185.101369
## 281 185.741414
## 282 186.381459
## 283 187.021503
## 284 187.661548
## 285 188.301593
## 286 188.941638
## 287 189.581683
## 288 190.221728
## 289 190.861773
## 290 191.501818
## 291 192.141863
## 292 192.781907
## 293 193.421952
## 294 194.061997
## 295 194.702042
## 296 195.342087
## 297 195.982132
## 298 196.622177
## 299 197.262222
## 300 197.902267
test<-read.csv("E:\\Data science\\Practies\\slrtest.csv")
View(test)
final<-predict(m1,newdata=test)
final
## 1 2 3 4 5 6
## 9.089024 11.009159 7.168889 9.729069 10.369114 9.089024