### Setup
getwd()
## [1] "C:/Users/Jerome/Documents/0000_Work_Files/0000_Montgomery_College/Data_Science_101/Data_101_Fall_2022/Homework_12_Due_28Nov28/IC11_Regression_Practice"
library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
library(dplyr)
library(psych)
## Warning: package 'psych' was built under R version 4.2.2
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
library(infer)
library(ggplot2)
### Read the Data
day <- read_csv("day.csv")
## Rows: 731 Columns: 16
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (15): instant, season, yr, mnth, holiday, weekday, workingday, weathers...
## date (1): dteday
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
### Examine the Data
str(day)
## spec_tbl_df [731 × 16] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ instant : num [1:731] 1 2 3 4 5 6 7 8 9 10 ...
## $ dteday : Date[1:731], format: "2011-01-01" "2011-01-02" ...
## $ season : num [1:731] 1 1 1 1 1 1 1 1 1 1 ...
## $ yr : num [1:731] 0 0 0 0 0 0 0 0 0 0 ...
## $ mnth : num [1:731] 1 1 1 1 1 1 1 1 1 1 ...
## $ holiday : num [1:731] 0 0 0 0 0 0 0 0 0 0 ...
## $ weekday : num [1:731] 6 0 1 2 3 4 5 6 0 1 ...
## $ workingday: num [1:731] 0 0 1 1 1 1 1 0 0 1 ...
## $ weathersit: num [1:731] 2 2 1 1 1 1 2 2 1 1 ...
## $ temp : num [1:731] 0.344 0.363 0.196 0.2 0.227 ...
## $ atemp : num [1:731] 0.364 0.354 0.189 0.212 0.229 ...
## $ hum : num [1:731] 0.806 0.696 0.437 0.59 0.437 ...
## $ windspeed : num [1:731] 0.16 0.249 0.248 0.16 0.187 ...
## $ casual : num [1:731] 331 131 120 108 82 88 148 68 54 41 ...
## $ registered: num [1:731] 654 670 1229 1454 1518 ...
## $ cnt : num [1:731] 985 801 1349 1562 1600 ...
## - attr(*, "spec")=
## .. cols(
## .. instant = col_double(),
## .. dteday = col_date(format = ""),
## .. season = col_double(),
## .. yr = col_double(),
## .. mnth = col_double(),
## .. holiday = col_double(),
## .. weekday = col_double(),
## .. workingday = col_double(),
## .. weathersit = col_double(),
## .. temp = col_double(),
## .. atemp = col_double(),
## .. hum = col_double(),
## .. windspeed = col_double(),
## .. casual = col_double(),
## .. registered = col_double(),
## .. cnt = col_double()
## .. )
## - attr(*, "problems")=<externalptr>
head(day)
## # A tibble: 6 × 16
## instant dteday season yr mnth holiday weekday workingday weath…¹ temp
## <dbl> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 2011-01-01 1 0 1 0 6 0 2 0.344
## 2 2 2011-01-02 1 0 1 0 0 0 2 0.363
## 3 3 2011-01-03 1 0 1 0 1 1 1 0.196
## 4 4 2011-01-04 1 0 1 0 2 1 1 0.2
## 5 5 2011-01-05 1 0 1 0 3 1 1 0.227
## 6 6 2011-01-06 1 0 1 0 4 1 1 0.204
## # … with 6 more variables: atemp <dbl>, hum <dbl>, windspeed <dbl>,
## # casual <dbl>, registered <dbl>, cnt <dbl>, and abbreviated variable name
## # ¹​weathersit
tail(day)
## # A tibble: 6 × 16
## instant dteday season yr mnth holiday weekday workingday weath…¹ temp
## <dbl> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 726 2012-12-26 1 1 12 0 3 1 3 0.243
## 2 727 2012-12-27 1 1 12 0 4 1 2 0.254
## 3 728 2012-12-28 1 1 12 0 5 1 2 0.253
## 4 729 2012-12-29 1 1 12 0 6 0 2 0.253
## 5 730 2012-12-30 1 1 12 0 0 0 1 0.256
## 6 731 2012-12-31 1 1 12 0 1 1 2 0.216
## # … with 6 more variables: atemp <dbl>, hum <dbl>, windspeed <dbl>,
## # casual <dbl>, registered <dbl>, cnt <dbl>, and abbreviated variable name
## # ¹​weathersit
summary(day)
## instant dteday season yr
## Min. : 1.0 Min. :2011-01-01 Min. :1.000 Min. :0.0000
## 1st Qu.:183.5 1st Qu.:2011-07-02 1st Qu.:2.000 1st Qu.:0.0000
## Median :366.0 Median :2012-01-01 Median :3.000 Median :1.0000
## Mean :366.0 Mean :2012-01-01 Mean :2.497 Mean :0.5007
## 3rd Qu.:548.5 3rd Qu.:2012-07-01 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :731.0 Max. :2012-12-31 Max. :4.000 Max. :1.0000
## mnth holiday weekday workingday
## Min. : 1.00 Min. :0.00000 Min. :0.000 Min. :0.000
## 1st Qu.: 4.00 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.000
## Median : 7.00 Median :0.00000 Median :3.000 Median :1.000
## Mean : 6.52 Mean :0.02873 Mean :2.997 Mean :0.684
## 3rd Qu.:10.00 3rd Qu.:0.00000 3rd Qu.:5.000 3rd Qu.:1.000
## Max. :12.00 Max. :1.00000 Max. :6.000 Max. :1.000
## weathersit temp atemp hum
## Min. :1.000 Min. :0.05913 Min. :0.07907 Min. :0.0000
## 1st Qu.:1.000 1st Qu.:0.33708 1st Qu.:0.33784 1st Qu.:0.5200
## Median :1.000 Median :0.49833 Median :0.48673 Median :0.6267
## Mean :1.395 Mean :0.49538 Mean :0.47435 Mean :0.6279
## 3rd Qu.:2.000 3rd Qu.:0.65542 3rd Qu.:0.60860 3rd Qu.:0.7302
## Max. :3.000 Max. :0.86167 Max. :0.84090 Max. :0.9725
## windspeed casual registered cnt
## Min. :0.02239 Min. : 2.0 Min. : 20 Min. : 22
## 1st Qu.:0.13495 1st Qu.: 315.5 1st Qu.:2497 1st Qu.:3152
## Median :0.18097 Median : 713.0 Median :3662 Median :4548
## Mean :0.19049 Mean : 848.2 Mean :3656 Mean :4504
## 3rd Qu.:0.23321 3rd Qu.:1096.0 3rd Qu.:4776 3rd Qu.:5956
## Max. :0.50746 Max. :3410.0 Max. :6946 Max. :8714
### Question 4 Response Variable
### 2 options: cnt, the total count of riders on a given day, and registered, the count of registered riders in a given day.
total <- sum(day$cnt)
members <- sum(day$registered)
nonmem <- sum(day$casual)
members + nonmem
## [1] 3292679
nonmem/total
## [1] 0.1883017
### Because casual riders are nearly 20% of the total number of riders, it would make sense to use cnt as the dependent variable. The percentage of casual riders seems to be the same, whether on an overall basis or a daily basis, on average.
total/731
## [1] 4504.349
nonmem/731
## [1] 848.1765
848/4504
## [1] 0.1882771
### Question 5 Linear Model
lin_model <- lm(formula = cnt ~ weathersit, data = day)
lin_model
##
## Call:
## lm(formula = cnt ~ weathersit, data = day)
##
## Coefficients:
## (Intercept) weathersit
## 5980 -1057
### Question 6 Scatterplot w/ line of best fit
plot(day$weathersit, day$cnt, pch = 16, col = "red", xlab = "Weather Conditions", ylab = "Number of Riders",
main = "Ridership vs. Weather Conditions")
abline(lm(cnt ~ weathersit, data = day), lwd = 2)
summary(lin_model)
##
## Call:
## lm(formula = cnt ~ weathersit, data = day)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4491.3 -1285.8 -45.1 1421.3 4496.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5979.6 188.3 31.75 <2e-16 ***
## weathersit -1057.3 125.7 -8.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1851 on 729 degrees of freedom
## Multiple R-squared: 0.08844, Adjusted R-squared: 0.08719
## F-statistic: 70.73 on 1 and 729 DF, p-value: < 2.2e-16
### Question 7 Statistical significance of the model.
### Yes, the model is statistically significant, given the t-value of the weathersit coefficient (-8.41) and its p-value (2e -16)
### Coefficients:
#### Estimate Std. Error t value Pr(>|t|)
####(Intercept) 5979.6 188.3 31.75 <2e-16 ***
####weathersit -1057.3 125.7 -8.41 <2e-16 ***
### Questions 8 and 9 Correlation coefficient and r squared
#### R-squared: 0.08844
#### Correlation coefficient is the square root of R-Squared or 0.2974
#### This means the weather conditions are weakly and negatively correlated w/ ridership; weather conditions explain about 8% of the variation in ridership in the bikeshare program.
sqrt(.08844)
## [1] 0.2973886
### Question 10 Plot the residuals
res <- residuals(lin_model); res
## 1 2 3 4 5 6
## -2880.059013 -3064.059013 -3573.346030 -3360.346030 -3322.346030 -3316.346030
## 7 8 9 10 11 12
## -2355.059013 -2906.059013 -4100.346030 -3601.346030 -2602.059013 -3760.346030
## 13 14 15 16 17 18
## -3516.346030 -3501.346030 -2617.059013 -3718.346030 -2865.059013 -3182.059013
## 19 20 21 22 23 24
## -2215.059013 -1938.059013 -3379.346030 -3941.346030 -3936.346030 -3506.346030
## 25 26 27 28 29 30
## -1880.059013 -2301.771996 -4491.346030 -2698.059013 -3824.346030 -3826.346030
## 31 32 33 34 35 36
## -2364.059013 -2505.059013 -2339.059013 -3372.346030 -2157.059013 -2860.059013
## 37 38 39 40 41 42
## -3299.346030 -3210.346030 -3392.346030 -2260.059013 -3384.346030 -3176.346030
## 43 44 45 46 47 48
## -3450.346030 -3333.346030 -3009.346030 -3107.346030 -2807.346030 -2447.346030
## 49 50 51 52 53 54
## -1995.346030 -3287.346030 -3110.346030 -2758.059013 -3472.346030 -3005.346030
## 55 56 57 58 59 60
## -2058.059013 -2404.059013 -2953.346030 -2520.346030 -2419.059013 -3071.346030
## 61 62 63 64 65 66
## -2788.346030 -3237.346030 -1921.059013 -1788.059013 -3260.059013 -3050.346030
## 67 68 69 70 71 72
## -2789.346030 -1974.059013 -2184.771996 -1888.059013 -2790.346030 -2505.346030
## 73 74 75 76 77 78
## -2876.346030 -1809.059013 -1673.059013 -2178.346030 -1683.346030 -1805.346030
## 79 80 81 82 83 84
## -2451.346030 -1788.059013 -2219.346030 -1744.059013 -2000.059013 -2712.346030
## 85 86 87 88 89 90
## -2426.346030 -2172.059013 -2894.346030 -2497.346030 -2329.059013 -1122.771996
## 91 92 93 94 95 96
## -1638.059013 -1613.059013 -1673.346030 -1807.346030 -2070.059013 -2114.346030
## 97 98 99 100 101 102
## -1781.346030 -2394.059013 -1410.059013 -970.059013 -517.059013 -1831.059013
## 103 104 105 106 107 108
## -1703.059013 -1655.346030 -1796.346030 -2012.771996 -1178.346030 -1493.346030
## 109 110 111 112 113 114
## -661.059013 -978.346030 -733.346030 -2182.059013 170.940987 325.940987
## 115 116 117 118 119 120
## -849.346030 -522.346030 6.940987 192.940987 -327.346030 389.653970
## 121 122 123 124 125 126
## -514.059013 535.940987 585.940987 -1232.059013 -489.346030 -314.346030
## 127 128 129 130 131 132
## -208.346030 -589.346030 -560.346030 -119.346030 -740.346030 -58.346030
## 133 134 135 136 137 138
## 239.940987 -456.059013 687.940987 -964.346030 257.940987 -10.059013
## 139 140 141 142 143 144
## 709.940987 -5.346030 882.653970 -262.346030 408.940987 626.940987
## 145 146 147 148 149 150
## 55.653970 -245.346030 -243.346030 -164.346030 -134.346030 -824.346030
## 151 152 153 154 155 156
## -940.346030 108.940987 45.653970 389.653970 419.653970 1040.940987
## 157 158 159 160 161 162
## -374.346030 -89.346030 -521.346030 49.940987 -336.346030 43.653970
## 163 164 165 166 167 168
## -462.346030 97.653970 -31.346030 257.653970 -98.059013 -78.346030
## 169 170 171 172 173 174
## 196.653970 878.940987 144.940987 969.940987 -415.346030 924.940987
## 175 176 177 178 179 180
## 68.653970 279.653970 382.653970 842.940987 -274.346030 302.653970
## 181 182 183 184 185 186
## 592.653970 439.653970 196.653970 783.940987 2177.940987 -257.346030
## 187 188 189 190 191 192
## -293.346030 -330.346030 174.940987 413.653970 -41.346030 -836.346030
## 193 194 195 196 197 198
## -664.346030 -580.346030 161.653970 615.653970 1000.653970 379.653970
## 199 200 201 202 203 204
## -464.346030 -381.346030 -590.346030 -81.059013 -1535.346030 -1637.346030
## 205 206 207 208 209 210
## -1316.346030 -1082.346030 -332.346030 -266.346030 -532.346030 -1076.346030
## 211 212 213 214 215 216
## -447.346030 -620.346030 -656.346030 -77.346030 -291.059013 710.940987
## 217 218 219 220 221 222
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## 223 224 225 226 227 228
## -130.346030 -17.346030 284.940987 -45.059013 -584.346030 -197.346030
## 229 230 231 232 233 234
## -228.346030 -1117.346030 287.940987 268.653970 -1049.346030 -164.346030
## 235 236 237 238 239 240
## 972.653970 207.653970 -323.059013 -261.346030 -2750.059013 -588.346030
## 241 242 243 244 245 246
## -288.346030 281.653970 135.653970 192.653970 861.940987 -438.346030
## 247 248 249 250 251 252
## 17.653970 -514.059013 -97.771996 -811.771996 -965.771996 -321.059013
## 253 254 255 256 257 258
## 422.653970 123.653970 -209.346030 -159.346030 -137.346030 -206.059013
## 259 260 261 262 263 264
## 894.940987 645.940987 -648.346030 673.940987 -224.059013 486.940987
## 265 266 267 268 269 270
## 929.940987 -1470.059013 1557.940987 1144.940987 764.940987 254.940987
## 271 272 273 274 275 276
## 41.940987 -83.346030 279.653970 -1436.059013 -947.059013 -295.059013
## 277 278 279 280 281 282
## -466.346030 -96.346030 -157.346030 62.653970 486.653970 588.653970
## 283 284 285 286 287 288
## 194.653970 697.940987 -391.771996 -952.059013 -221.059013 294.653970
## 289 290 291 292 293 294
## 118.653970 -352.346030 882.940987 -383.771996 -727.346030 -618.346030
## 295 296 297 298 299 300
## -614.346030 -541.346030 -735.346030 -235.346030 28.940987 -1206.059013
## 301 302 303 304 305 306
## -118.059013 -2180.771996 -1591.346030 -1253.346030 -854.346030 -736.346030
## 307 308 309 310 311 312
## -948.346030 180.940987 -996.346030 -1273.346030 -887.346030 -717.346030
## 313 314 315 316 317 318
## -813.346030 -932.059013 -1554.346030 -855.346030 -1205.346030 -436.346030
## 319 320 321 322 323 324
## 329.940987 -990.771996 -812.059013 -1530.346030 -1259.346030 -345.059013
## 325 326 327 328 329 330
## -42.771996 -1200.771996 -1299.059013 -3427.346030 -2130.346030 -1854.346030
## 331 332 333 334 335 336
## -1851.346030 -1055.346030 -951.059013 -1309.346030 -1195.346030 -982.346030
## 337 338 339 340 341 342
## -1308.346030 -1437.346030 -54.059013 -213.771996 -2102.771996 -1600.346030
## 343 344 345 346 347 348
## -1302.346030 -1732.346030 -2179.346030 -1612.346030 -1399.346030 -125.059013
## 349 350 351 352 353 354
## -156.059013 -288.059013 -1126.059013 -2491.346030 -1519.346030 -115.059013
## 355 356 357 358 359 360
## -1205.059013 -797.059013 -2713.346030 -3911.346030 -4168.346030 -3605.346030
## 361 362 363 364 365 366
## -2703.059013 -2620.346030 -2499.346030 -1923.346030 -2437.346030 -2628.346030
## 367 368 369 370 371 372
## -2971.346030 -2686.346030 -1497.059013 -1650.346030 -824.346030 -401.346030
## 373 374 375 376 377 378
## -1497.346030 -1489.059013 -1324.346030 -1688.059013 231.940987 -1708.346030
## 379 380 381 382 383 384
## -2429.346030 -2611.346030 -2624.346030 -930.059013 -1546.346030 -1630.346030
## 385 386 387 388 389 390
## -702.059013 -2564.059013 -1888.059013 -1433.059013 -583.346030 -652.346030
## 391 392 393 394 395 396
## 209.940987 -409.059013 -899.346030 -1679.346030 -1298.346030 -413.346030
## 397 398 399 400 401 402
## -343.346030 -104.059013 -771.346030 -1033.059013 -918.059013 -1138.346030
## 403 404 405 406 407 408
## -547.346030 -1063.059013 -1092.346030 -34.059013 -638.771996 -3393.346030
## 409 410 411 412 413 414
## -1500.346030 56.940987 -753.346030 -860.059013 -768.346030 -604.346030
## 415 416 417 418 419 420
## -1176.059013 -1793.346030 -1145.346030 -149.346030 139.653970 -378.059013
## 421 422 423 424 425 426
## -2190.346030 -1533.346030 -600.346030 -559.346030 -2031.059013 67.653970
## 427 428 429 430 431 432
## -671.059013 200.940987 -1499.346030 -1589.346030 -966.346030 -6.346030
## 433 434 435 436 437 438
## 459.653970 703.940987 -804.346030 -11.346030 375.653970 924.653970
## 439 440 441 442 443 444
## 1389.653970 1269.653970 512.940987 3970.940987 2026.940987 1230.653970
## 445 446 447 448 449 450
## 1170.653970 2364.940987 1948.653970 4496.940987 -493.059013 1130.940987
## 451 452 453 454 455 456
## 635.653970 179.653970 775.653970 1210.653970 1593.940987 2369.940987
## 457 458 459 460 461 462
## 2175.940987 1013.653970 1849.653970 1513.653970 1534.653970 1537.653970
## 463 464 465 466 467 468
## 1934.653970 246.653970 662.653970 995.653970 -60.346030 486.653970
## 469 470 471 472 473 474
## 1475.653970 2537.653970 2209.653970 1447.653970 1768.653970 501.940987
## 475 476 477 478 479 480
## 1642.653970 2367.653970 1701.653970 -1780.771996 -651.059013 710.653970
## 481 482 483 484 485 486
## 1273.653970 1160.940987 1310.653970 354.940987 1381.653970 1706.940987
## 487 488 489 490 491 492
## 1874.940987 1246.653970 2555.940987 1373.653970 3017.940987 2493.940987
## 493 494 495 496 497 498
## 2407.940987 1862.940987 851.940987 1649.653970 2107.653970 2506.653970
## 499 500 501 502 503 504
## 1195.653970 -1022.059013 1249.940987 2501.653970 2461.653970 2716.653970
## 505 506 507 508 509 510
## 3371.653970 2206.653970 493.940987 2207.940987 1394.940987 1847.653970
## 511 512 513 514 515 516
## 1811.653970 1613.653970 1668.653970 1120.653970 820.653970 2989.940987
## 517 518 519 520 521 522
## 2415.653970 261.940987 3197.653970 2718.653970 2075.653970 3135.940987
## 523 524 525 526 527 528
## 2132.653970 2571.653970 2813.653970 2575.653970 1675.653970 2798.940987
## 529 530 531 532 533 534
## 1106.940987 2498.653970 2440.653970 2742.653970 2779.653970 2055.653970
## 535 536 537 538 539 540
## 1233.940987 1902.653970 1288.653970 982.653970 900.653970 2535.653970
## 541 542 543 544 545 546
## 1968.653970 1856.653970 2519.653970 2412.653970 1956.653970 540.653970
## 547 548 549 550 551 552
## 764.653970 608.653970 1304.653970 1737.653970 2480.653970 1318.653970
## 553 554 555 556 557 558
## 1284.653970 -82.346030 -250.346030 2703.940987 2424.940987 2341.653970
## 559 560 561 562 563 564
## 2523.653970 3633.940987 3103.940987 1108.653970 1907.653970 1863.653970
## 565 566 567 568 569 570
## 790.653970 1668.653970 2004.940987 1651.228004 3544.940987 2043.653970
## 571 572 573 574 575 576
## 2669.653970 3250.653970 1938.653970 1981.653970 1762.653970 1674.653970
## 577 578 579 580 581 582
## 2182.653970 2293.653970 2657.653970 2338.653970 3309.940987 1901.653970
## 583 584 585 586 587 588
## 541.653970 3147.940987 3407.940987 3668.940987 2363.653970 1920.940987
## 589 590 591 592 593 594
## 2433.940987 1621.653970 1960.653970 1861.653970 2424.653970 2682.653970
## 595 596 597 598 599 600
## 2225.653970 2942.653970 683.940987 2664.940987 2083.653970 2452.653970
## 601 602 603 604 605 606
## 2842.653970 3716.940987 2187.940987 1389.940987 1994.653970 2117.653970
## 607 608 609 610 611 612
## 2774.653970 2790.653970 2427.653970 2274.940987 1944.940987 1111.653970
## 613 614 615 616 617 618
## 1941.653970 2189.653970 2337.940987 2581.653970 2110.940987 3304.653970
## 619 620 621 622 623 624
## 2602.653970 2844.653970 2947.653970 2881.653970 3086.653970 3791.653970
## 625 626 627 628 629 630
## 2410.653970 3003.940987 207.940987 2668.653970 2797.653970 3244.653970
## 631 632 633 634 635 636
## 3472.653970 2984.653970 2513.653970 2615.653970 2810.653970 3527.940987
## 637 638 639 640 641 642
## 3549.940987 3632.653970 1966.653970 2912.940987 1831.228004 3706.940987
## 643 644 645 646 647 648
## 3462.940987 3233.653970 3042.653970 -355.059013 1612.940987 2526.940987
## 649 650 651 652 653 654
## 2768.653970 2647.653970 2359.653970 2186.653970 1716.653970 2009.940987
## 655 656 657 658 659 660
## 2611.653970 2538.653970 3643.940987 1558.940987 3167.653970 1901.653970
## 661 662 663 664 665 666
## 2135.653970 2543.653970 2770.653970 3493.940987 3578.940987 3986.940987
## 667 668 669 670 671 672
## 593.940987 -2785.771996 -2769.059013 1700.940987 2120.940987 924.653970
## 673 674 675 676 677 678
## 1272.940987 184.653970 336.653970 763.653970 1169.940987 392.653970
## 679 680 681 682 683 684
## 1069.653970 1613.653970 1929.653970 1346.653970 228.940987 572.653970
## 685 686 687 688 689 690
## 1579.940987 775.653970 706.653970 -253.346030 1633.940987 1768.940987
## 691 692 693 694 695 696
## 223.653970 -2497.346030 -1012.346030 -2645.346030 -2498.346030 164.653970
## 697 698 699 700 701 702
## 93.940987 337.653970 400.653970 745.653970 1325.940987 783.940987
## 703 704 705 706 707 708
## 1311.653970 1683.653970 806.653970 452.653970 1142.940987 1716.940987
## 709 710 711 712 713 714
## -637.059013 1304.940987 1635.940987 1453.940987 609.653970 688.653970
## 715 716 717 718 719 720
## 124.653970 -79.059013 719.940987 634.653970 344.653970 262.940987
## 721 722 723 724 725 726
## -242.059013 -3173.346030 -3135.346030 -2945.059013 -2852.059013 -2366.771996
## 727 728 729 730 731
## -1751.059013 -770.059013 -2524.059013 -3126.346030 -1136.059013
plot(day$weathersit, res, ylab = 'Residual', xlab = 'Weather Conditions', pch = 16,
main = "Residuals for Ridership vs. Weather Conditions")
abline(0, 0, lwd = 2)
#### The residuals do appear to be randomly distributed, normally.
### Question 11 Meeting the assumptions
#### The assumptions of the linear regression model are these: Linearity, Homoskedasticity, Independence, Normality. The results of this run appear to meet those assumptions.