Group 2 Case Study 1
Johna Delos Reyes, Jenelle Uy, Justin Zhao
2024-03-17
data <- read.csv("Household energy bill data.csv")I. Introduction
Background of the Study
Electricity is a fundamental input into powering the systems within residential properties. Being able to consume electricity helps improve one’s style of living at the expense of the environment (Zhang et al., 2017). To combat the potential effects of climate change, governments need to enact relevant energy regulations to encourage efficient energy consumption (Zhang et al., 2017). Nilsson et al. (2017) reported that a third of global electricity demand is consumed by residential households while the services and industrial sectors share 19% and 53%, respectively. While the industrial sector holds the highest share of electricity consumption, companies have their own ways to voluntarily reduce electricity consumption. The same goes for the services sector with the objective of growing profit. Therefore, there is a need to study the residential sector since it does not necessarily reduce electricity consumption voluntarily. Understanding the factors that influence the electricity consumption of households can help policymakers craft relevant energy regulations to encourage reduced energy consumption.
The utilization of data-driven approaches, such as regression modeling, offers valuable insights into the factors influencing residential energy consumption patterns. By identifying significant predictors, policymakers can tailor interventions to promote energy efficiency and reduce electricity bills for households. Thus, investigating the relationship between household characteristics and electricity consumption aligns with broader efforts to achieve sustainable energy practices.
Objective
This study aims to achieve the following objectives: 1. To create desciptive visuals or statistical visuals such as scatter plots and correlation, to provide comprehemsive understanding of the relationships between the variables 2. To create a model using stepwise regression that will determine or predict the insurance premiums according to the independent variables 3. To create a model using multiple linear regression that will examine the correlation between the independent variables and the dependent variables 4. To assess the accuracy of the models created
Statement of the Problem
The study aims to investigate the factors influencing monthly electricity consumption in households. It seeks to analyze the impact of various household and house characteristics, including the number of rooms, house area, presence of appliances, average monthly income, and number of children, on the monthly energy bill. By examining these factors, this study aims to address the following main research question: How do different household and house characteristics influence the monthly electricity consumption of households?
Hypotheses
Null Hypothesis (H0): There is no significant relationship between the dependent variable (amount_paid) and the independent variables (num_people, housearea, is_tv, is_ac, is_flat, ave_monthly_income, num_children, is_urban).
Alternative Hypothesis (H1): There is a significant relationship between the dependent variable (amount_paid) and the independent variables (num_people, housearea, is_tv, is_ac, is_flat, ave_monthly_income, num_children, is_urban).
III. Descriptive Statistics
class(data)## [1] "data.frame"str(data)## 'data.frame': 1000 obs. of 10 variables:
## $ num_rooms : int 3 1 3 0 1 0 4 3 2 1 ...
## $ num_people : int 3 5 1 5 8 5 5 4 4 6 ...
## $ housearea : num 743 953 761 861 732 ...
## $ is_ac : int 1 0 1 1 0 0 0 0 1 0 ...
## $ is_tv : int 1 1 1 1 1 1 1 0 0 0 ...
## $ is_flat : int 1 0 1 0 0 1 0 1 0 0 ...
## $ ave_monthly_income: num 9676 35065 22292 12139 17230 ...
## $ num_children : int 2 1 0 0 2 2 1 2 0 2 ...
## $ is_urban : int 0 1 0 0 1 1 1 1 1 1 ...
## $ amount_paid : num 560 633 512 333 658 ...dplyr::glimpse(data)## Rows: 1,000
## Columns: 10
## $ num_rooms <int> 3, 1, 3, 0, 1, 0, 4, 3, 2, 1, 2, 1, 0, 2, 2, 1, 3, …
## $ num_people <int> 3, 5, 1, 5, 8, 5, 5, 4, 4, 6, 6, 6, 3, 4, 7, 5, 5, …
## $ housearea <dbl> 742.57, 952.99, 761.44, 861.32, 731.61, 837.24, 679…
## $ is_ac <int> 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, …
## $ is_tv <int> 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, …
## $ is_flat <int> 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, …
## $ ave_monthly_income <dbl> 9675.93, 35064.79, 22292.44, 12139.08, 17230.10, 24…
## $ num_children <int> 2, 1, 0, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 0, 1, 0, 3, …
## $ is_urban <int> 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, …
## $ amount_paid <dbl> 560.4814, 633.2837, 511.8792, 332.9920, 658.2856, 7…summary(data)## num_rooms num_people housearea is_ac
## Min. :-1.000 Min. :-1.000 Min. : 244.4 Min. :0.000
## 1st Qu.: 1.000 1st Qu.: 4.000 1st Qu.: 691.0 1st Qu.:0.000
## Median : 2.000 Median : 5.000 Median : 790.0 Median :0.000
## Mean : 1.962 Mean : 4.897 Mean : 794.7 Mean :0.376
## 3rd Qu.: 3.000 3rd Qu.: 6.000 3rd Qu.: 893.0 3rd Qu.:1.000
## Max. : 5.000 Max. :11.000 Max. :1189.1 Max. :1.000
## is_tv is_flat ave_monthly_income num_children
## Min. :0.000 Min. :0.000 Min. :-1576 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:18037 1st Qu.:0.000
## Median :1.000 Median :0.000 Median :24743 Median :1.000
## Mean :0.798 Mean :0.477 Mean :24685 Mean :1.078
## 3rd Qu.:1.000 3rd Qu.:1.000 3rd Qu.:31402 3rd Qu.:2.000
## Max. :1.000 Max. :1.000 Max. :56531 Max. :4.000
## is_urban amount_paid
## Min. :0.000 Min. : 87.85
## 1st Qu.:0.000 1st Qu.: 475.07
## Median :1.000 Median : 598.33
## Mean :0.608 Mean : 600.40
## 3rd Qu.:1.000 3rd Qu.: 729.93
## Max. :1.000 Max. :1102.99Tables for Categorical Variables
table(data$is_ac); table (data$is_tv);##
## 0 1
## 624 376##
## 0 1
## 202 798table(data$is_flat); table(data$is_urban)##
## 0 1
## 523 477##
## 0 1
## 392 608Above, we can see the tables for the categorical variables in the dataset. 1 indicates those who qualify for the given characters as mentioned whicle 0 signify the other. For is the electric devices contributing to the bill, there are 376 answered yes for the AC while 624 ansewered no while as for TV, there are significantly more people who answered yes as it is 798 while only 202 answered no. Moving on the characteristics of the area of living, there are more people who said they don’t live in a flat garnerning 523 votes while only 477 live in flats. Lastly, there are a lot more people who lives in the urban area as 608 people said yes and only 392 said no.
psych::describe(data)psych::describeBy(data, data$num_people)##
## Descriptive statistics by group
## group: -1
## vars n mean sd median trimmed mad min
## num_rooms 1 4 2.50 1.29 2.50 2.50 1.48 1.00
## num_people 2 4 -1.00 0.00 -1.00 -1.00 0.00 -1.00
## housearea 3 4 782.63 202.96 738.69 782.63 154.82 594.82
## is_ac 4 4 0.25 0.50 0.00 0.25 0.00 0.00
## is_tv 5 4 0.75 0.50 1.00 0.75 0.00 0.00
## is_flat 6 4 0.50 0.58 0.50 0.50 0.74 0.00
## ave_monthly_income 7 4 27033.30 7701.81 28037.55 27033.30 7255.75 17182.76
## num_children 8 4 1.25 1.89 0.50 1.25 0.74 0.00
## is_urban 9 4 0.75 0.50 1.00 0.75 0.00 0.00
## amount_paid 10 4 538.23 50.79 534.69 538.23 54.93 484.60
## max range skew kurtosis se
## num_rooms 4.00 3.00 0.00 -2.08 0.65
## num_people -1.00 0.00 NaN NaN 0.00
## housearea 1058.32 463.50 0.39 -1.94 101.48
## is_ac 1.00 1.00 0.75 -1.69 0.25
## is_tv 1.00 1.00 -0.75 -1.69 0.25
## is_flat 1.00 1.00 0.00 -2.44 0.29
## ave_monthly_income 34875.33 17692.57 -0.23 -2.04 3850.91
## num_children 4.00 4.00 0.62 -1.79 0.95
## is_urban 1.00 1.00 -0.75 -1.69 0.25
## amount_paid 598.94 114.34 0.11 -2.15 25.39
## ------------------------------------------------------------
## group: 0
## vars n mean sd median trimmed mad min
## num_rooms 1 13 2.62 0.77 3.00 2.64 0.00 1.00
## num_people 2 13 0.00 0.00 0.00 0.00 0.00 0.00
## housearea 3 13 840.34 183.83 797.67 836.26 131.79 549.85
## is_ac 4 13 0.46 0.52 0.00 0.45 0.00 0.00
## is_tv 5 13 0.77 0.44 1.00 0.82 0.00 0.00
## is_flat 6 13 0.62 0.51 1.00 0.64 0.00 0.00
## ave_monthly_income 7 13 24772.57 9160.53 24223.22 24505.63 9135.83 12317.68
## num_children 8 13 1.15 0.90 1.00 1.18 1.48 0.00
## is_urban 9 13 0.85 0.38 1.00 0.91 0.00 0.00
## amount_paid 10 13 697.10 155.81 709.07 724.80 78.88 238.90
## max range skew kurtosis se
## num_rooms 4.00 3.00 -0.36 -0.52 0.21
## num_people 0.00 0.00 NaN NaN 0.00
## housearea 1175.71 625.86 0.24 -1.16 50.99
## is_ac 1.00 1.00 0.14 -2.13 0.14
## is_tv 1.00 1.00 -1.13 -0.76 0.12
## is_flat 1.00 1.00 -0.42 -1.96 0.14
## ave_monthly_income 40163.85 27846.17 0.29 -1.22 2540.67
## num_children 2.00 2.00 -0.27 -1.80 0.25
## is_urban 1.00 1.00 -1.70 0.99 0.10
## amount_paid 850.62 611.72 -1.79 2.91 43.21
## ------------------------------------------------------------
## group: 1
## vars n mean sd median trimmed mad min
## num_rooms 1 33 2.06 0.97 2.00 2.11 1.48 0.00
## num_people 2 33 1.00 0.00 1.00 1.00 0.00 1.00
## housearea 3 33 798.39 147.98 808.88 801.53 140.46 515.34
## is_ac 4 33 0.33 0.48 0.00 0.30 0.00 0.00
## is_tv 5 33 0.73 0.45 1.00 0.78 0.00 0.00
## is_flat 6 33 0.45 0.51 0.00 0.44 0.00 0.00
## ave_monthly_income 7 33 22898.67 8572.32 22346.64 22789.89 8787.93 7525.82
## num_children 8 33 0.94 0.83 1.00 0.89 1.48 0.00
## is_urban 9 33 0.52 0.51 1.00 0.52 0.00 0.00
## amount_paid 10 33 531.72 152.01 535.70 530.02 183.13 272.87
## max range skew kurtosis se
## num_rooms 4.00 4.00 -0.32 -0.65 0.17
## num_people 1.00 0.00 NaN NaN 0.00
## housearea 1077.31 561.97 -0.20 -0.97 25.76
## is_ac 1.00 1.00 0.68 -1.59 0.08
## is_tv 1.00 1.00 -0.97 -1.08 0.08
## is_flat 1.00 1.00 0.17 -2.03 0.09
## ave_monthly_income 40260.49 32734.67 0.10 -0.64 1492.25
## num_children 3.00 3.00 0.43 -0.70 0.14
## is_urban 1.00 1.00 -0.06 -2.06 0.09
## amount_paid 813.74 540.88 0.13 -1.06 26.46
## ------------------------------------------------------------
## group: 2
## vars n mean sd median trimmed mad min
## num_rooms 1 72 1.79 1.01 2.00 1.81 1.48 -1.00
## num_people 2 72 2.00 0.00 2.00 2.00 0.00 2.00
## housearea 3 72 796.60 130.24 767.43 788.63 127.17 516.37
## is_ac 4 72 0.44 0.50 0.00 0.43 0.00 0.00
## is_tv 5 72 0.82 0.39 1.00 0.90 0.00 0.00
## is_flat 6 72 0.51 0.50 1.00 0.52 0.00 0.00
## ave_monthly_income 7 72 23761.73 8843.90 24221.15 23924.47 8881.03 37.78
## num_children 8 72 1.11 0.99 1.00 1.03 1.48 0.00
## is_urban 9 72 0.60 0.49 1.00 0.62 0.00 0.00
## amount_paid 10 72 604.92 162.57 598.19 601.90 137.79 224.59
## max range skew kurtosis se
## num_rooms 4.00 5.00 -0.07 -0.02 0.12
## num_people 2.00 0.00 NaN NaN 0.00
## housearea 1136.00 619.63 0.51 -0.29 15.35
## is_ac 1.00 1.00 0.22 -1.98 0.06
## is_tv 1.00 1.00 -1.63 0.66 0.05
## is_flat 1.00 1.00 -0.05 -2.02 0.06
## ave_monthly_income 46993.00 46955.22 -0.09 -0.10 1042.26
## num_children 4.00 4.00 0.48 -0.50 0.12
## is_urban 1.00 1.00 -0.39 -1.87 0.06
## amount_paid 1018.81 794.22 0.18 -0.06 19.16
## ------------------------------------------------------------
## group: 3
## vars n mean sd median trimmed mad min
## num_rooms 1 96 2.01 1.07 2.00 2.00 1.48 0.00
## num_people 2 96 3.00 0.00 3.00 3.00 0.00 3.00
## housearea 3 96 790.93 151.63 776.86 791.93 147.74 443.63
## is_ac 4 96 0.34 0.48 0.00 0.31 0.00 0.00
## is_tv 5 96 0.82 0.38 1.00 0.90 0.00 0.00
## is_flat 6 96 0.42 0.50 0.00 0.40 0.00 0.00
## ave_monthly_income 7 96 24262.36 9544.91 24666.29 24105.45 11005.15 1220.02
## num_children 8 96 1.16 0.97 1.00 1.09 1.48 0.00
## is_urban 9 96 0.60 0.49 1.00 0.63 0.00 0.00
## amount_paid 10 96 579.97 173.64 562.67 585.17 158.04 97.54
## max range skew kurtosis se
## num_rooms 5.00 5.00 0.13 -0.34 0.11
## num_people 3.00 0.00 NaN NaN 0.00
## housearea 1118.29 674.66 0.00 -0.47 15.48
## is_ac 1.00 1.00 0.65 -1.60 0.05
## is_tv 1.00 1.00 -1.67 0.78 0.04
## is_flat 1.00 1.00 0.33 -1.91 0.05
## ave_monthly_income 49294.85 48074.83 0.11 -0.38 974.17
## num_children 3.00 3.00 0.24 -1.08 0.10
## is_urban 1.00 1.00 -0.42 -1.84 0.05
## amount_paid 915.47 817.93 -0.20 -0.20 17.72
## ------------------------------------------------------------
## group: 4
## vars n mean sd median trimmed mad
## num_rooms 1 187 1.92 0.97 2.00 1.89 1.48
## num_people 2 187 4.00 0.00 4.00 4.00 0.00
## housearea 3 187 807.87 144.54 794.74 804.18 142.54
## is_ac 4 187 0.30 0.46 0.00 0.25 0.00
## is_tv 5 187 0.77 0.42 1.00 0.83 0.00
## is_flat 6 187 0.44 0.50 0.00 0.42 0.00
## ave_monthly_income 7 187 25480.34 11028.43 25193.60 25445.58 11493.49
## num_children 8 187 1.10 0.88 1.00 1.06 1.48
## is_urban 9 187 0.68 0.47 1.00 0.73 0.00
## amount_paid 10 187 603.38 172.81 598.52 600.53 159.63
## min max range skew kurtosis se
## num_rooms 0.00 4.00 4.00 0.23 -0.18 0.07
## num_people 4.00 4.00 0.00 NaN NaN 0.00
## housearea 485.29 1185.36 700.07 0.24 -0.27 10.57
## is_ac 0.00 1.00 1.00 0.87 -1.25 0.03
## is_tv 0.00 1.00 1.00 -1.27 -0.38 0.03
## is_flat 0.00 1.00 1.00 0.25 -1.95 0.04
## ave_monthly_income -1177.42 56531.08 57708.50 0.08 -0.07 806.48
## num_children 0.00 3.00 3.00 0.28 -0.81 0.06
## is_urban 0.00 1.00 1.00 -0.79 -1.39 0.03
## amount_paid 152.81 1022.60 869.80 0.16 -0.19 12.64
## ------------------------------------------------------------
## group: 5
## vars n mean sd median trimmed mad min
## num_rooms 1 224 1.90 1.09 2.00 1.92 1.48 -1.00
## num_people 2 224 5.00 0.00 5.00 5.00 0.00 5.00
## housearea 3 224 778.91 157.42 778.52 778.46 161.20 244.40
## is_ac 4 224 0.38 0.49 0.00 0.36 0.00 0.00
## is_tv 5 224 0.80 0.40 1.00 0.88 0.00 0.00
## is_flat 6 224 0.50 0.50 0.50 0.50 0.74 0.00
## ave_monthly_income 7 224 25106.43 9302.86 26217.44 25180.88 9178.12 -1013.85
## num_children 8 224 1.04 0.94 1.00 0.94 1.48 0.00
## is_urban 9 224 0.56 0.50 1.00 0.58 0.00 0.00
## amount_paid 10 224 588.22 207.94 582.97 585.93 230.75 87.85
## max range skew kurtosis se
## num_rooms 5.00 6.00 0.01 -0.40 0.07
## num_people 5.00 0.00 NaN NaN 0.00
## housearea 1189.12 944.72 -0.11 0.14 10.52
## is_ac 1.00 1.00 0.47 -1.78 0.03
## is_tv 1.00 1.00 -1.52 0.31 0.03
## is_flat 1.00 1.00 0.00 -2.01 0.03
## ave_monthly_income 47904.37 48918.22 -0.14 -0.15 621.57
## num_children 3.00 3.00 0.55 -0.63 0.06
## is_urban 1.00 1.00 -0.25 -1.95 0.03
## amount_paid 1094.76 1006.91 0.10 -0.67 13.89
## ------------------------------------------------------------
## group: 6
## vars n mean sd median trimmed mad min
## num_rooms 1 174 1.98 1.01 2.00 1.96 1.48 0.00
## num_people 2 174 6.00 0.00 6.00 6.00 0.00 6.00
## housearea 3 174 789.20 143.57 788.26 790.31 142.49 361.13
## is_ac 4 174 0.40 0.49 0.00 0.38 0.00 0.00
## is_tv 5 174 0.78 0.42 1.00 0.84 0.00 0.00
## is_flat 6 174 0.50 0.50 0.50 0.50 0.74 0.00
## ave_monthly_income 7 174 23787.30 9439.65 22769.45 23566.13 9867.36 -1576.44
## num_children 8 174 1.11 1.01 1.00 0.99 1.48 0.00
## is_urban 9 174 0.58 0.49 1.00 0.60 0.00 0.00
## amount_paid 10 174 602.76 186.09 603.33 604.65 191.61 175.89
## max range skew kurtosis se
## num_rooms 5.00 5.00 0.23 -0.04 0.08
## num_people 6.00 0.00 NaN NaN 0.00
## housearea 1129.49 768.36 -0.10 0.06 10.88
## is_ac 1.00 1.00 0.40 -1.85 0.04
## is_tv 1.00 1.00 -1.31 -0.28 0.03
## is_flat 1.00 1.00 0.00 -2.01 0.04
## ave_monthly_income 47483.47 49059.91 0.19 -0.30 715.62
## num_children 4.00 4.00 0.65 -0.26 0.08
## is_urban 1.00 1.00 -0.32 -1.91 0.04
## amount_paid 1102.99 927.11 -0.01 -0.42 14.11
## ------------------------------------------------------------
## group: 7
## vars n mean sd median trimmed mad min
## num_rooms 1 104 2.09 0.97 2.00 2.12 1.48 0.00
## num_people 2 104 7.00 0.00 7.00 7.00 0.00 7.00
## housearea 3 104 797.56 142.35 806.61 799.24 157.42 478.33
## is_ac 4 104 0.37 0.48 0.00 0.33 0.00 0.00
## is_tv 5 104 0.85 0.36 1.00 0.93 0.00 0.00
## is_flat 6 104 0.48 0.50 0.00 0.48 0.00 0.00
## ave_monthly_income 7 104 25605.47 9763.12 25669.60 25539.26 10163.16 -526.54
## num_children 8 104 0.97 0.88 1.00 0.90 1.48 0.00
## is_urban 9 104 0.64 0.48 1.00 0.68 0.00 0.00
## amount_paid 10 104 618.82 162.06 630.76 621.70 161.90 226.46
## max range skew kurtosis se
## num_rooms 4.00 4.00 -0.23 -0.44 0.09
## num_people 7.00 0.00 NaN NaN 0.00
## housearea 1130.50 652.17 -0.09 -0.61 13.96
## is_ac 1.00 1.00 0.55 -1.71 0.05
## is_tv 1.00 1.00 -1.89 1.59 0.04
## is_flat 1.00 1.00 0.08 -2.01 0.05
## ave_monthly_income 49063.95 49590.49 0.02 -0.24 957.35
## num_children 3.00 3.00 0.49 -0.67 0.09
## is_urban 1.00 1.00 -0.59 -1.66 0.05
## amount_paid 976.82 750.36 -0.16 -0.47 15.89
## ------------------------------------------------------------
## group: 8
## vars n mean sd median trimmed mad min
## num_rooms 1 54 2.02 1.14 2.00 2.07 1.48 -1.00
## num_people 2 54 8.00 0.00 8.00 8.00 0.00 8.00
## housearea 3 54 784.06 137.94 792.98 782.72 162.11 518.49
## is_ac 4 54 0.54 0.50 1.00 0.55 0.00 0.00
## is_tv 5 54 0.85 0.36 1.00 0.93 0.00 0.00
## is_flat 6 54 0.43 0.50 0.00 0.41 0.00 0.00
## ave_monthly_income 7 54 23038.59 9078.73 22968.41 22768.94 9951.20 4577.68
## num_children 8 54 1.07 0.93 1.00 0.98 1.48 0.00
## is_urban 9 54 0.57 0.50 1.00 0.59 0.00 0.00
## amount_paid 10 54 639.65 171.78 670.07 645.37 179.43 273.60
## max range skew kurtosis se
## num_rooms 4.00 5.00 -0.48 0.15 0.16
## num_people 8.00 0.00 NaN NaN 0.00
## housearea 1055.17 536.68 0.07 -0.98 18.77
## is_ac 1.00 1.00 -0.14 -2.02 0.07
## is_tv 1.00 1.00 -1.93 1.74 0.05
## is_flat 1.00 1.00 0.29 -1.95 0.07
## ave_monthly_income 50110.52 45532.84 0.36 -0.01 1235.46
## num_children 4.00 4.00 0.83 0.53 0.13
## is_urban 1.00 1.00 -0.29 -1.95 0.07
## amount_paid 961.68 688.08 -0.31 -0.56 23.38
## ------------------------------------------------------------
## group: 9
## vars n mean sd median trimmed mad min
## num_rooms 1 28 1.79 1.03 2.00 1.75 1.48 0.00
## num_people 2 28 9.00 0.00 9.00 9.00 0.00 9.00
## housearea 3 28 860.13 137.06 850.00 858.29 152.42 572.76
## is_ac 4 28 0.39 0.50 0.00 0.38 0.00 0.00
## is_tv 5 28 0.82 0.39 1.00 0.88 0.00 0.00
## is_flat 6 28 0.54 0.51 1.00 0.54 0.00 0.00
## ave_monthly_income 7 28 26224.54 7141.07 26320.66 26245.03 5404.08 10770.83
## num_children 8 28 1.25 0.93 1.00 1.21 1.48 0.00
## is_urban 9 28 0.61 0.50 1.00 0.62 0.00 0.00
## amount_paid 10 28 632.07 179.83 615.61 633.67 190.37 262.13
## max range skew kurtosis se
## num_rooms 4.00 4.00 0.22 -0.23 0.19
## num_people 9.00 0.00 NaN NaN 0.00
## housearea 1123.53 550.77 0.08 -0.71 25.90
## is_ac 1.00 1.00 0.42 -1.89 0.09
## is_tv 1.00 1.00 -1.59 0.55 0.07
## is_flat 1.00 1.00 -0.14 -2.05 0.10
## ave_monthly_income 44083.19 33312.36 0.17 0.16 1349.54
## num_children 3.00 3.00 0.05 -1.12 0.18
## is_urban 1.00 1.00 -0.42 -1.89 0.09
## amount_paid 992.32 730.19 -0.14 -0.69 33.98
## ------------------------------------------------------------
## group: 10
## vars n mean sd median trimmed mad min
## num_rooms 1 9 2.00 1.22 2.00 2.00 1.48 0.00
## num_people 2 9 10.00 0.00 10.00 10.00 0.00 10.00
## housearea 3 9 808.36 188.37 858.17 808.36 239.40 496.23
## is_ac 4 9 0.33 0.50 0.00 0.33 0.00 0.00
## is_tv 5 9 0.67 0.50 1.00 0.67 0.00 0.00
## is_flat 6 9 0.44 0.53 0.00 0.44 0.00 0.00
## ave_monthly_income 7 9 23171.91 12738.47 24743.19 23171.91 17065.19 6031.98
## num_children 8 9 1.00 0.50 1.00 1.00 0.00 0.00
## is_urban 9 9 0.44 0.53 0.00 0.44 0.00 0.00
## amount_paid 10 9 569.14 161.90 505.92 569.14 99.42 408.76
## max range skew kurtosis se
## num_rooms 3.00 3.00 -0.73 -1.22 0.41
## num_people 10.00 0.00 NaN NaN 0.00
## housearea 1064.73 568.50 -0.25 -1.41 62.79
## is_ac 1.00 1.00 0.59 -1.81 0.17
## is_tv 1.00 1.00 -0.59 -1.81 0.17
## is_flat 1.00 1.00 0.19 -2.17 0.18
## ave_monthly_income 40972.21 34940.23 0.09 -1.71 4246.16
## num_children 2.00 2.00 0.00 0.56 0.17
## is_urban 1.00 1.00 0.19 -2.17 0.18
## amount_paid 819.69 410.93 0.59 -1.53 53.97
## ------------------------------------------------------------
## group: 11
## vars n mean sd median trimmed mad min
## num_rooms 1 2 2.00 1.41 2.00 2.00 1.48 1.00
## num_people 2 2 11.00 0.00 11.00 11.00 0.00 11.00
## housearea 3 2 751.18 276.56 751.18 751.18 289.94 555.62
## is_ac 4 2 0.00 0.00 0.00 0.00 0.00 0.00
## is_tv 5 2 0.50 0.71 0.50 0.50 0.74 0.00
## is_flat 6 2 1.00 0.00 1.00 1.00 0.00 1.00
## ave_monthly_income 7 2 40792.07 16932.43 40792.07 40792.07 17751.22 28819.03
## num_children 8 2 1.00 1.41 1.00 1.00 1.48 0.00
## is_urban 9 2 1.00 0.00 1.00 1.00 0.00 1.00
## amount_paid 10 2 605.70 175.92 605.70 605.70 184.42 481.31
## max range skew kurtosis se
## num_rooms 3.00 2.00 0 -2.75 1.00
## num_people 11.00 0.00 NaN NaN 0.00
## housearea 946.74 391.12 0 -2.75 195.56
## is_ac 0.00 0.00 NaN NaN 0.00
## is_tv 1.00 1.00 0 -2.75 0.50
## is_flat 1.00 0.00 NaN NaN 0.00
## ave_monthly_income 52765.10 23946.07 0 -2.75 11973.03
## num_children 2.00 2.00 0 -2.75 1.00
## is_urban 1.00 0.00 NaN NaN 0.00
## amount_paid 730.09 248.78 0 -2.75 124.39The best suit for this dataset is the “psych” package for describing a household electrivity monthly bill dataset due to its versatile tools for statistical analysis. In this dataset, representing household monthly bill information, several key variables provide insights into the characteristics of the households. On average, households have approximately 1.96 rooms, and the number of rooms ranges from 1 to 5, with a median of 2. The average household size is about 4.90 people, ranging from 2 to 11, with a median of 5. The average household area is 794.70 square units, varying between 244.40 and 1189.12 square units, and a median of 789.97. About 38% of households have air conditioning, and around 80% have a TV. Additionally, approximately 48% of households live in flats. The average monthly income is $24,684.99, with incomes ranging from -$1,576.44 to $58,107.52 and a median of $24,742.57. On average, households have around 1.08 children, ranging from 0 to 4, with a median of 1. About 61% of households are located in urban areas. Lastly, the average monthly bill payment is $600.40, ranging from $87.85 to $1,102.99, with a median of $598.33.
cor(data$num_children, data$amount_paid)## [1] 0.4475123psych::pairs.panels(data)
Conducting the correlation analysis through the pairs.panels, we can see that the one with the highest correlation with the amount_paid dependent variable is the is_urban variable which is a categorical variable with 0.65. With the numerical values, we can see that the number of children is the one with the highest correlation with 0.45 to our DV. Meanwhile, number of rooms has the lowest correlation with the DV, with only -0.02.
bill1 <- data [ , -c(4:6,9)]
psych::pairs.panels(bill1)
While as for here, we made a new dataset containing only the numerical variables which will make a better reference looking at the numerical values that affects our Dependent Variable. Conducting the same analysis as earlier, we can see the same data but only with the numerical values. It retains the same information as earlier, only with the values
##Plotting the Data
attach(data)
plot(num_children, amount_paid, main = "scatterplot of num_children and amount_paid")
detach(data)Conducting a scatterplot with the number of children and amount paid by the household, we can see that as the number of children increase, the amount paid for the electricity also increases as we can the range by each children adding slightly going up.
IV. Model Creation Using Backward Stepwise Regression
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversmod1 <- lm(amount_paid ~., data = data)
summary(mod1)##
## Call:
## lm(formula = amount_paid ~ ., data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -120.294 -53.617 -0.841 52.174 120.337
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.208e+02 1.463e+01 8.253 4.89e-16 ***
## num_rooms -1.095e-01 1.939e+00 -0.056 0.95496
## num_people 4.828e+00 9.948e-01 4.853 1.41e-06 ***
## housearea 3.919e-02 1.359e-02 2.883 0.00403 **
## is_ac 1.632e+02 4.129e+00 39.525 < 2e-16 ***
## is_tv 7.548e+01 4.992e+00 15.121 < 2e-16 ***
## is_flat 5.976e+01 3.995e+00 14.957 < 2e-16 ***
## ave_monthly_income 1.034e-03 2.065e-04 5.008 6.52e-07 ***
## num_children 9.037e+01 2.140e+00 42.228 < 2e-16 ***
## is_urban 2.500e+02 4.098e+00 61.013 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 63.04 on 990 degrees of freedom
## Multiple R-squared: 0.8803, Adjusted R-squared: 0.8792
## F-statistic: 809.2 on 9 and 990 DF, p-value: < 2.2e-16jtools::summ(mod1)## MODEL INFO:
## Observations: 1000
## Dependent Variable: amount_paid
## Type: OLS linear regression
##
## MODEL FIT:
## F(9,990) = 809.20, p = 0.00
## R² = 0.88
## Adj. R² = 0.88
##
## Standard errors: OLS
## ---------------------------------------------------------
## Est. S.E. t val. p
## ------------------------ -------- ------- -------- ------
## (Intercept) 120.77 14.63 8.25 0.00
## num_rooms -0.11 1.94 -0.06 0.95
## num_people 4.83 0.99 4.85 0.00
## housearea 0.04 0.01 2.88 0.00
## is_ac 163.21 4.13 39.53 0.00
## is_tv 75.48 4.99 15.12 0.00
## is_flat 59.76 4.00 14.96 0.00
## ave_monthly_income 0.00 0.00 5.01 0.00
## num_children 90.37 2.14 42.23 0.00
## is_urban 250.01 4.10 61.01 0.00
## ---------------------------------------------------------(bwdfit.p <- ols_step_backward_p(mod1, pent = .05, prem = .05, details = TRUE))## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . num_rooms
## 2 . num_people
## 3 . housearea
## 4 . is_ac
## 5 . is_tv
## 6 . is_flat
## 7 . ave_monthly_income
## 8 . num_children
## 9 . is_urban
##
## We are eliminating variables based on p value...
##
## - num_rooms
##
## Backward Elimination: Step 1
##
## Variable num_rooms Removed
##
## Model Summary
## ----------------------------------------------------------------
## R 0.938 RMSE 63.007
## R-Squared 0.880 Coef. Var 10.494
## Adj. R-Squared 0.879 MSE 3969.919
## Pred R-Squared 0.878 MAE 53.638
## ----------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 28941114.476 8 3617639.309 911.263 0.0000
## Residual 3934190.219 991 3969.919
## Total 32875304.695 999
## --------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------
## (Intercept) 120.523 13.975 8.624 0.000 93.098 147.948
## num_people 4.828 0.994 0.053 4.856 0.000 2.877 6.779
## housearea 0.039 0.014 0.032 2.888 0.004 0.013 0.066
## is_ac 163.208 4.127 0.436 39.551 0.000 155.110 171.305
## is_tv 75.486 4.989 0.167 15.130 0.000 65.696 85.277
## is_flat 59.755 3.993 0.165 14.964 0.000 51.919 67.591
## ave_monthly_income 0.001 0.000 0.055 5.010 0.000 0.001 0.001
## num_children 90.374 2.138 0.465 42.279 0.000 86.179 94.569
## is_urban 250.012 4.095 0.673 61.050 0.000 241.976 258.048
## --------------------------------------------------------------------------------------------------
##
##
##
## No more variables satisfy the condition of p value = 0.05
##
##
## Variables Removed:
##
## - num_rooms
##
##
## Final Model Output
## ------------------
##
## Model Summary
## ----------------------------------------------------------------
## R 0.938 RMSE 63.007
## R-Squared 0.880 Coef. Var 10.494
## Adj. R-Squared 0.879 MSE 3969.919
## Pred R-Squared 0.878 MAE 53.638
## ----------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## --------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## --------------------------------------------------------------------------
## Regression 28941114.476 8 3617639.309 911.263 0.0000
## Residual 3934190.219 991 3969.919
## Total 32875304.695 999
## --------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------------
## (Intercept) 120.523 13.975 8.624 0.000 93.098 147.948
## num_people 4.828 0.994 0.053 4.856 0.000 2.877 6.779
## housearea 0.039 0.014 0.032 2.888 0.004 0.013 0.066
## is_ac 163.208 4.127 0.436 39.551 0.000 155.110 171.305
## is_tv 75.486 4.989 0.167 15.130 0.000 65.696 85.277
## is_flat 59.755 3.993 0.165 14.964 0.000 51.919 67.591
## ave_monthly_income 0.001 0.000 0.055 5.010 0.000 0.001 0.001
## num_children 90.374 2.138 0.465 42.279 0.000 86.179 94.569
## is_urban 250.012 4.095 0.673 61.050 0.000 241.976 258.048
## --------------------------------------------------------------------------------------------------##
##
## Elimination Summary
## ----------------------------------------------------------------------------
## Variable Adj.
## Step Removed R-Square R-Square C(p) AIC RMSE
## ----------------------------------------------------------------------------
## 1 num_rooms 0.8803 0.8794 8.0032 11135.3374 63.0073
## ----------------------------------------------------------------------------modfinal <- lm(amount_paid ~ num_people + housearea + is_tv + is_ac + is_flat + ave_monthly_income + num_children + is_urban, data = data)summary(modfinal)##
## Call:
## lm(formula = amount_paid ~ num_people + housearea + is_tv + is_ac +
## is_flat + ave_monthly_income + num_children + is_urban, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -120.18 -53.58 -0.87 52.09 120.33
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.205e+02 1.398e+01 8.624 < 2e-16 ***
## num_people 4.828e+00 9.943e-01 4.856 1.39e-06 ***
## housearea 3.921e-02 1.358e-02 2.888 0.00397 **
## is_tv 7.549e+01 4.989e+00 15.130 < 2e-16 ***
## is_ac 1.632e+02 4.127e+00 39.551 < 2e-16 ***
## is_flat 5.975e+01 3.993e+00 14.964 < 2e-16 ***
## ave_monthly_income 1.034e-03 2.064e-04 5.010 6.43e-07 ***
## num_children 9.037e+01 2.138e+00 42.279 < 2e-16 ***
## is_urban 2.500e+02 4.095e+00 61.050 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 63.01 on 991 degrees of freedom
## Multiple R-squared: 0.8803, Adjusted R-squared: 0.8794
## F-statistic: 911.3 on 8 and 991 DF, p-value: < 2.2e-16jtools :: summ(modfinal)## MODEL INFO:
## Observations: 1000
## Dependent Variable: amount_paid
## Type: OLS linear regression
##
## MODEL FIT:
## F(8,991) = 911.26, p = 0.00
## R² = 0.88
## Adj. R² = 0.88
##
## Standard errors: OLS
## ---------------------------------------------------------
## Est. S.E. t val. p
## ------------------------ -------- ------- -------- ------
## (Intercept) 120.52 13.98 8.62 0.00
## num_people 4.83 0.99 4.86 0.00
## housearea 0.04 0.01 2.89 0.00
## is_tv 75.49 4.99 15.13 0.00
## is_ac 163.21 4.13 39.55 0.00
## is_flat 59.75 3.99 14.96 0.00
## ave_monthly_income 0.00 0.00 5.01 0.00
## num_children 90.37 2.14 42.28 0.00
## is_urban 250.01 4.10 61.05 0.00
## ---------------------------------------------------------confint(modfinal)## 2.5 % 97.5 %
## (Intercept) 9.309783e+01 1.479476e+02
## num_people 2.876889e+00 6.779198e+00
## housearea 1.256295e-02 6.585822e-02
## is_tv 6.569557e+01 8.527666e+01
## is_ac 1.551098e+02 1.713054e+02
## is_flat 5.191862e+01 6.759105e+01
## ave_monthly_income 6.292315e-04 1.439435e-03
## num_children 8.617924e+01 9.456867e+01
## is_urban 2.419757e+02 2.580482e+02library(performance)
citation("performance")## To cite package 'performance' in publications use:
##
## Lüdecke et al., (2021). performance: An R Package for Assessment,
## Comparison and Testing of Statistical Models. Journal of Open Source
## Software, 6(60), 3139. https://doi.org/10.21105/joss.03139
##
## A BibTeX entry for LaTeX users is
##
## @Article{,
## title = {{performance}: An {R} Package for Assessment, Comparison and Testing of Statistical Models},
## author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski},
## year = {2021},
## journal = {Journal of Open Source Software},
## volume = {6},
## number = {60},
## pages = {3139},
## doi = {10.21105/joss.03139},
## }compare_performance(mod1, modfinal, rank = 1)anova(mod1)anova(modfinal)V. Discussion of Results
Discussion of the Final Model
The objective of this study is to know the factors that influence the household energy bills. We fitted a linear regression model using ordinary least squares (OLS) to predict the dependent variable “amount_paid”. The predictors in the model are num_people, housearea, is_ac, is_tv, is_flat, ave_monthly_income, num_children, and is_urban. The final formula for this model is amount_paid ~ num_people + housearea + is_ac + is_tv + is_flat + ave_monthly_income + num_children + is_urban. The model appears to explain a significant proportion of the variance in amount_paid (R2 = 0.880, F(8, 991) = 911.26, p < .001, adj. R2 = 0.879). The variable num_rooms was removed as it got the highest p value among all the variables.
The model’s intercept corresponding to num_people = 0, housearea = 0, ave_monthly_income = 0, num_children = 0, is_ac = 0, is_tv = 0, is_flat = 0, is_urban = 0, is at 120.52 (95% CI [9.31 , 1.48], t(991) = 8.62, P < .001 ) Within this model:
- the effect of num_people is statistically significant and postive (beta = 4.83, 95% CI [2.88, 6.78], t(521) = 4.86, p < .001)
- the effect of housearea is statistically significant and postive (beta = 0.04, 95% CI [1.26, 6.59], t(521) = 2.89, p < .001)
- the effect of is_tv is statistically significant and positive (beta = 75.49, 95% CI [6.57, 8.53], t(521) = 15.13, p < .001)
- the effect of is_ac is statistically significant and positive (beta = 163.21, 95% CI [1.55, 1.71], t(521) = 39.55, p < .001)
- the effect of is_flat is statistically significant and positive (beta = 59.75, 95% CI [5.19, 6.76], t(521) = 14.96, p < .001)
- the effect of ave_monthly_income is statistically significant and postive (beta = 0, 95% CI [6.29, 1.44], t(521) = 5.01, p < .001)
- the effect of num_children is statistically significant and positive (beta = 90.37 CI [8.62, 9.46], t(521) = 42.28, p < .001)
- the effect of is_urban is statistically significant and positive (beta = 250.01 CI[2.42, 2.58], t(521) = 61.05, p < .001)
Each predictor variable in the final model shows statistical significance, indicating that all the independent variables are significantly associated with the total amount paid for energy bills. For example, for every one-person increase, the predicted amount paid for the energy bill increases by $4.38 ceteris paribus. Moreover, for every one-unit increase in house area, the predicted amount paid for the energy bill will increase by $0.04 ceteris paribus. For an additional television, there will be an increase of $75.49 in the energy bill ceteris paribus. Similarly, with an additional unit of air conditioner, there will be an increase of $163.21 in the energy bill ceteris paribus. When the average monthly income increases every year, then the energy bill will also increase by $0 ceteris paribus. The $0 increase in the energy bill might indicate that there is no effect on the amount paid for the energy bill regardless of the increase in monthly income. When a family has another child, the energy bill will increase by $90.37 ceteris paribus. Lastly, with an increase in housing in an urban area, there will be a $250.01 increase ceteris paribus.
Comparison of the Models
In the compare_performance section, the table displayed both AIC and BIC, R², Adj R², RMSE, and Sigma. The AIC and BIC values are lower for the final model, indicating that modfinal is much better than mod1. Moreover, both models have similar R² and Adj R² values, indicating that they explain a comparable amount of variance in the dependent variable.
In the ANOVA test, it showed that all the independent variables are statistically significant predictors for the dependent variable (amount_paid). The low p-value indicates that there is a low probability of observing weak relationships between the independent variables and the dependent variable (amount_paid). Moreover, the high F-statistic value indicates a significant relationship between the independent variables and the dependent variable.
VI. Model Diagnostics
plot(modfinal)
plot(modfinal, which = 1)
car::crPlots(modfinal)
The scatterplot demonstrates a linear relationship between the dependent variable and the independent variables. Furthermore, the points are randomly distributed around the regression line. The residuals remain constant across the fitted values, indicating that the assumption of homoscedasticity is met.
H0: Residuals variance is constant.
lmtest::bptest(modfinal)##
## studentized Breusch-Pagan test
##
## data: modfinal
## BP = 3.4156, df = 8, p-value = 0.9056plot(modfinal, 2)
We fail to reject the null hypothesis since the p-value exceeds the
significance level (alpha) of 0.05. Rejecting the null hypothesis would
indicate evidence of non-constant residuals or heteroscedasticity in the
final model. However, as the assumption of homoscedasticity is met, it
confirms the reliability of the standard errors or residuals in the
regression model. The result from the Normal QQ plot showed that the
dataset is uniformly distributed. The pattern showed that the outliers
are less likely to occur. This also suggests that the values in the
dataset are relatively spread out across the range.
performance::check_heteroscedasticity(modfinal)## OK: Error variance appears to be homoscedastic (p = 0.956).The result showed that the final model appears to be homoscedastic as the p-value of the final model is 0.956. Since the p-value is greater than the significant level of 0.05, there is no significant evidence of heteroscedasticity in the final model. As a consequence, the assuption about homoscedasticity is met. This means that the standard errors or the outliers of the regression model are reliable.
ols_plot_resid_hist(modfinal) 
ols_test_correlation(modfinal)## [1] 0.983584The result of the correlation is 0.983584 means that the model has a strong liinear relationship between the independent variables and dependent variable.
car:: vif(modfinal)## num_people housearea is_tv is_ac
## 1.002674 1.013272 1.010714 1.006384
## is_flat ave_monthly_income num_children is_urban
## 1.002059 1.004492 1.003553 1.006827All the independent variables resulted in VIF values of 1, indicating that the independent variables are not correlated with each other. This shows that the model does not have multicollinearity.
VII. Conclusion and Recommendations
Conclusion
In summary, our case study investigates the factors influencing household electrical monthly bills. It collected data on various household attributes such as the number of rooms, number of people, presence of amenities like air conditioning and television, average monthly income, number of children, urban location status, and the amount paid for monthly bills. Using the collected data, a backward stepwise regression model was employed to identify the significant predictors of household monthly bills. The results of the stepwise regression model provided insights into the factors that most strongly influence household monthly bills such as the urban area and the number of children in the household. By systematically removing predictors, the model identified the subset of variables that best predict the variation in monthly bills. This helped in understanding which factors have the most significant impact on household expenditures.
Recommendations
We recommend conducting further research to explore additional factors that may influence household monthly bills, such as regional differences, lifestyle choices, or seasonal variations. This could provide a more comprehensive understanding of the determinants of household expenditures and inform future policy interventions. Additionally, policymakers can use the insights gained from the regression model to design targeted policies aimed at reducing household expenses. For instance, subsidies or incentives can be provided for energy-efficient upgrades or public transportation to reduce transportation costs for urban households. This way it will encourage households to engage in effective financial planning based on their average monthly income and other socioeconomic factors. Providing resources or workshops on budgeting and financial management can help households better allocate their resources and prioritize spending. Overall, the study demonstrated the utility of a backward stepwise regression model in identifying the key determinants of household monthly bills. By pinpointing the most influential factors, policymakers and households can better understand and manage their monthly expenses, leading to improved financial planning and decision-making.
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