About the Data

  • Hourly Rental Bike Usage in Washington DC
  • Data on season, day of the week, temperature, humidity, wind speed, weather, number of users, etc.

Exercise 1: summary statistics.

Solve:

  1. 1.1 Average number of total users
[1] 189.4631
  1. 1.2 Average temperature (in F)
[1] 58.77751
  1. 1.3 median Humidity
[1] 63
  1. 1.4 Variance of the Number of Registered Users
[1] 22909.03
  1. 1.5 Standard Deviation of the Number of Casual Users
[1] 49.30503

Exercise 2: Vizualization the Data Distribution

Instructions: - to include title: main - to change the color of lines: col - to change the label of y and x axes: ylab and xlab - to change the limit of y and x axes: ylim and xlim


  1. 2.1 Density plot of Humidity

  1. 2.2 Density Plot of the Temperature including the mean and the median

  2. 2.3 Histogram of Wind Speed

  3. 2.4 Boxplot of Casual Users Including a line with the mean

Exercise 3: Normal Distribution

  1. 3.1 Generate a normal distribution with 1000 observations, mean = 20 and sd = 3 and then plot its density plot (Use the code set.seed(320) before)

  2. 3.2 Present the Histogram of this normal distribution

  3. 3.3 Present the Boxplot of this normal distribution

Excersise 4: Covariance and Correlation

  1. 4.1 Covariance between temperature and Total Number of Users
[1] 1220.347
  1. 4.2 Correlation between “Feels Like” Temperature and Total Number of Users
[1] 0.4009377
  1. 4.3 Correlation Matrix of bike data
                          Season         Hour      Holiday Day.of.the.Week
Season               1.000000000  0.004931139  0.055947939    -0.003163450
Hour                 0.004931139  1.000000000  0.000479136    -0.003497739
Holiday              0.055947939  0.000479136  1.000000000    -0.102087791
Day.of.the.Week     -0.003163450 -0.003497739 -0.102087791     1.000000000
Working.Day         -0.036158734  0.002284998 -0.252471370     0.035955071
Weather.Type         0.040452288 -0.020202528 -0.017036113     0.003310740
Temperature.F       -0.470806327  0.137625946 -0.027356343    -0.001805613
Temperature.Feels.F -0.469271254  0.133758276 -0.030974740    -0.008817003
Humidity             0.014750149 -0.276497828 -0.010588465    -0.037158268
Wind.Speed          -0.038741686  0.137253208  0.003984692     0.011504125
Casual.Users        -0.227260165  0.301201730  0.031563628     0.032721415
Registered.Users    -0.099585576  0.374140710 -0.047345424     0.021577888
Total.Users         -0.144872483  0.394071498 -0.030927303     0.026899860
                     Working.Day Weather.Type Temperature.F Temperature.Feels.F
Season              -0.036158734   0.04045229  -0.470806327        -0.469271254
Hour                 0.002284998  -0.02020253   0.137625946         0.133758276
Holiday             -0.252471370  -0.01703611  -0.027356343        -0.030974740
Day.of.the.Week      0.035955071   0.00331074  -0.001805613        -0.008817003
Working.Day          1.000000000   0.04467222   0.055396228         0.054665178
Weather.Type         0.044672224   1.00000000  -0.102600649        -0.105570718
Temperature.F        0.055396228  -0.10260065   1.000000000         0.987677449
Temperature.Feels.F  0.054665178  -0.10557072   0.987677449         1.000000000
Humidity             0.015687512   0.41813033  -0.069889709        -0.051935510
Wind.Speed          -0.011831470   0.02622604  -0.023115427        -0.062325722
Casual.Users        -0.300942486  -0.15262788   0.459626269         0.454088895
Registered.Users     0.134325791  -0.12096552   0.335373166         0.332565807
Total.Users          0.030284368  -0.14242614   0.404785441         0.400937689
                       Humidity   Wind.Speed Casual.Users Registered.Users
Season               0.01475015 -0.038741686  -0.22726017      -0.09958558
Hour                -0.27649783  0.137253208   0.30120173       0.37414071
Holiday             -0.01058846  0.003984692   0.03156363      -0.04734542
Day.of.the.Week     -0.03715827  0.011504125   0.03272142       0.02157789
Working.Day          0.01568751 -0.011831470  -0.30094249       0.13432579
Weather.Type         0.41813033  0.026226043  -0.15262788      -0.12096552
Temperature.F       -0.06988971 -0.023115427   0.45962627       0.33537317
Temperature.Feels.F -0.05193551 -0.062325722   0.45408890       0.33256581
Humidity             1.00000000 -0.290108894  -0.34702809      -0.27393312
Wind.Speed          -0.29010889  1.000000000   0.09029235       0.08232535
Casual.Users        -0.34702809  0.090292353   1.00000000       0.50661770
Registered.Users    -0.27393312  0.082325350   0.50661770       1.00000000
Total.Users         -0.32291074  0.093239057   0.69456408       0.97215073
                    Total.Users
Season              -0.14487248
Hour                 0.39407150
Holiday             -0.03092730
Day.of.the.Week      0.02689986
Working.Day          0.03028437
Weather.Type        -0.14242614
Temperature.F        0.40478544
Temperature.Feels.F  0.40093769
Humidity            -0.32291074
Wind.Speed           0.09323906
Casual.Users         0.69456408
Registered.Users     0.97215073
Total.Users          1.00000000

Excersise 5: Visualizing Two Variables

  1. 5.1 Plot Temperature in the x-axis and Total Number of Users in y-axis

  2. 5.2 Plot “Feels Like” Temperature in the x-axis and Number of Casual Users in y-axis, Include a line that indicates the correlation between these two variables (i.e., use the correlation as the slope of this line)

Exercise 6: Applied Questions.

  1. 6.1 Get the correlation between Temperature and “Feels Like” Temperature and interpret its value
[1] 0.9876774
  1. 6.2 Density Plot of Total Users including the mean and the median. Does this variable have a skew? If so, is it left of right skewed? Is it possible to know this just by looking at the mean and median? How?

  1. 6.3 Generate a normal with 10 observations, mean = 0 and sd = 1 (use set.seed = 99). Does this distribution looks like a normal? What would you have to do to make it look more like a normal distribution?

  1. 6.4 Provide the boxplot of Registered Users, What can you infer from this boxplot?