R Notebook

READING THE DATA

chicago_public_schools_test = read.csv(file = "Chicago_Public_Schools_Test.csv")
head(chicago_public_schools_test)

chicago_public_schools_train = read.csv(file = "Chicago_Public_Schools_Train.csv")
head(chicago_public_schools_train)

EXTRACTING VALUES

safety_score_train = chicago_public_schools_train$Safety.Score
family_involvement_score_train = chicago_public_schools_train$Family.Involvement.Score
environment_score_train = chicago_public_schools_train$Environment.Score
instruction_score_train = chicago_public_schools_train$Instruction.Score
leaders_score_train = chicago_public_schools_train$Leaders.Score
teachers_score_train = chicago_public_schools_train$Teachers.Score
parent_engagement_score_train = chicago_public_schools_train$Parent.Engagement.Score
parent_environment_score_train = chicago_public_schools_train$Parent.Environment.Score
avg_student_attendance_train = chicago_public_schools_train$Average.Student.Attendance
rate_of_misconduct_train = chicago_public_schools_train$Rate.of.Misconducts
avg_teacher_attendance_train = chicago_public_schools_train$Average.Teacher.Attendance
ISAT_exceeding_math_train = chicago_public_schools_train$ISAT.Exceeding.Math
ISAT_exceeding_reading_train = chicago_public_schools_train$ISAT.Exceeding.Reading
college_enrollment_train = chicago_public_schools_train$College.Enrollment
latitude_train = chicago_public_schools_train$Latitude
longitude_train = chicago_public_schools_train$Longitude
comm_area_number_train = chicago_public_schools_train$Community.Area.Number
ward_train = chicago_public_schools_train$Ward
police_district_train = chicago_public_schools_train$Police.District

BASIC MATH

mean_safety_score = mean(safety_score_train)
mean_safety_score

[1] 51.73

sd_safety_score = sd(safety_score_train)
sd_safety_score

[1] 20.88199

var_safety_score = var(safety_score_train)
var_safety_score

[1] 436.0577

sqrt()

Error in sqrt() : 0 arguments passed to 'sqrt' which requires 1

SIGNAL TO NOISE RATIO

snr_safety_score = safety_score_mean / safety_score_sd
snr_safety_score

[1] 2.477254

mean_environment_score = mean(environment_score_train)
mean_environment_score

[1] 51.11

sd_environment_score = sd(environment_score_train)
sd_environment_score

[1] 17.30703

snr_environment_score = mean_environment_score / sd_environment_score
snr_environment_score

[1] 2.953136

MAXIMUM, MINIMUM, AND RANGE

max_safety_score = max(safety_score_train)
max_safety_score

[1] 99

min_safety_score = min(safety_score_train)
min_safety_score

[1] 6

range_safety_score = max_safety_score - min_safety_score
range_safety_score

[1] 93

FINDING UPPER AND LOWER THRESHOLD FOR FINDING OUTLIERS

upper_threshold = mean_safety_score + 3*sd_safety_score
upper_threshold

[1] 114.376

lower_threshold = mean_safety_score - 3*sd_safety_score
lower_threshold

[1] -10.91598

environment_upper_threshold = mean_environment_score + 3*sd_environment_score
environment_upper_threshold

[1] 103.0311

environment_lower_threshold = mean_environment_score - 3*sd_environment_score
environment_lower_threshold

[1] -0.8110852

SUMMARY FUNCTION SPECIFIC (Can do for individual or whole data. Both shown below.)

summary(safety_score_train)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   6.00   35.75   50.00   51.73   61.75   99.00 

SUMMARY FUNCTION GENERAL

summary(chicago_public_schools_train)

   School.ID     
 Min.   :609772  
 1st Qu.:609878  
 Median :610008  
 Mean   :610033  
 3rd Qu.:610178  
 Max.   :610541  
                 
                                                         Name.of.School
 Abraham Lincoln Elementary School                              : 1    
 Adam Clayton Powell Paideia Community Academy Elementary School: 1    
 Agustin Lara Elementary Academy                                : 1    
 Albany Park Multicultural Academy                              : 1    
 Alessandro Volta Elementary School                             : 1    
 Alexander Graham Elementary School                             : 1    
 (Other)                                                        :94    
 Elementary_Middle_or_High.School              Street.Address      City    
 ES:96                            10041 S Union Ave   : 1     Chicago:100  
 MS: 4                            10115 S Prairie Ave : 1                  
                                  10538 S Langley Ave : 1                  
                                  10810 S Avenue H    : 1                  
                                  10845 S Union Ave   : 1                  
                                  (Other)             :92                  
                                  NA's                : 3                  
  State       ZIP.Code                         Network.Manager      Safety.Icon
 IL  :98   Min.   :60607   Pershing Elementary Network :11     Average    :40  
 NA's: 2   1st Qu.:60618   Midway Elementary Network   :10     Strong     :21  
           Median :60625   O'Hare Elementary Network   : 9     Very Strong:10  
           Mean   :60629   Fullerton Elementary Network: 8     Very Weak  : 3  
           3rd Qu.:60637   Skyway Elementary Network   : 8     Weak       :26  
           Max.   :60660   (Other)                     :47                     
                           NA's                        : 7                     
  Safety.Score   Family.Involvement.Icon Family.Involvement.Score
 Min.   : 6.00   Average    :39          Min.   :16.00           
 1st Qu.:35.75   Strong     :21          1st Qu.:38.00           
 Median :50.00   Very Strong: 9          Median :50.00           
 Mean   :51.73   Very Weak  : 2          Mean   :51.37           
 3rd Qu.:61.75   Weak       :29          3rd Qu.:62.25           
 Max.   :99.00                           Max.   :99.00           
                                                                 
    Environment.Icon Environment.Score    Instruction.Icon Instruction.Score
 Average    :45      Min.   : 2.00     Average    :44      Min.   : 1.00    
 Strong     :25      1st Qu.:40.00     Strong     :23      1st Qu.:39.75    
 Very Strong: 6      Median :50.00     Very Strong: 8      Median :50.00    
 Very Weak  : 2      Mean   :51.11     Very Weak  : 2      Mean   :52.08    
 Weak       :22      3rd Qu.:63.50     Weak       :23      3rd Qu.:63.00    
                     Max.   :99.00                         Max.   :99.00    
                                                                            
      Leaders.Icon Leaders.Score       Teachers.Icon Teachers.Score 
 Average    :37    Min.   :20.00   Average    :51    Min.   : 8.00  
 Strong     :28    1st Qu.:38.75   Strong     :19    1st Qu.:41.00  
 Very Strong: 8    Median :51.00   Very Strong: 7    Median :51.00  
 Weak       :27    Mean   :52.07   Very Weak  : 6    Mean   :51.08  
                   3rd Qu.:63.25   Weak       :17    3rd Qu.:61.00  
                   Max.   :97.00                     Max.   :99.00  
                                                                    
 Parent.Engagement.Icon Parent.Engagement.Score Parent.Environment.Icon
 Average:61             Min.   :43.0            Average:61             
 Strong :18             1st Qu.:47.0            Strong :19             
 Weak   :21             Median :50.0            Weak   :20             
                        Mean   :50.3                                   
                        3rd Qu.:52.0                                   
                        Max.   :68.0                                   
                                                                       
 Parent.Environment.Score Average.Student.Attendance Rate.of.Misconducts
 Min.   :38.00            95.50% : 8                 Min.   :  0.00     
 1st Qu.:47.00            95.10% : 6                 1st Qu.:  4.30     
 Median :50.00            95.60% : 5                 Median : 10.20     
 Mean   :50.04            92.50% : 4                 Mean   : 17.74     
 3rd Qu.:53.00            95.90% : 4                 3rd Qu.: 25.00     
 Max.   :65.00            93.40% : 3                 Max.   :100.50     
                          (Other):70                                    
 Average.Teacher.Attendance ISAT.Exceeding.Math ISAT.Exceeding.Reading
 95.90% : 6                 Min.   : 3.20       Min.   : 1.30         
 96.90% : 6                 1st Qu.:10.00       1st Qu.: 7.50         
 96.00% : 5                 Median :16.55       Median :11.60         
 96.10% : 5                 Mean   :21.83       Mean   :16.66         
 96.50% : 5                 3rd Qu.:25.68       3rd Qu.:19.80         
 94.70% : 4                 Max.   :92.80       Max.   :92.30         
 (Other):69                                                           
 College.Enrollment    Latitude       Longitude      Community.Area.Number
 Min.   : 192.0     Min.   :41.69   Min.   :-87.83   Min.   : 1.00        
 1st Qu.: 344.0     1st Qu.:41.76   1st Qu.:-87.71   1st Qu.:22.75        
 Median : 515.5     Median :41.84   Median :-87.68   Median :38.50        
 Mean   : 564.1     Mean   :41.84   Mean   :-87.68   Mean   :40.09        
 3rd Qu.: 717.2     3rd Qu.:41.91   3rd Qu.:-87.64   3rd Qu.:61.00        
 Max.   :1560.0     Max.   :42.01   Max.   :-87.53   Max.   :77.00        
                                                                          
         Community.Area.Name      Ward       Police.District
 WEST GARFIELD PARK: 5       Min.   : 1.00   Min.   : 1.00  
 WEST TOWN         : 5       1st Qu.:12.75   1st Qu.: 7.00  
 BRIGHTON PARK     : 4       Median :20.50   Median :10.00  
 ALBANY PARK       : 3       Mean   :22.31   Mean   :11.61  
 ASHBURN           : 3       3rd Qu.:30.25   3rd Qu.:17.00  
 AUBURN GRESHAM    : 3       Max.   :50.00   Max.   :25.00  
 (Other)           :77                                      
                        Location 
 (41.68733881, -87.70325179): 1  
 (41.68810403, -87.53600985): 1  
 (41.69093337, -87.65870614): 1  
 (41.69305404, -87.6808619) : 1  
 (41.69651565, -87.63993763): 1  
 (41.69719792, -87.6972638) : 1  
 (Other)                    :94  

BASIC PLOTTING

plot(safety_score_train)

Z VALUE (When X is a given value to test. In this example I chose 120)

x = 120
Zscore_safety_score = (x - mean_safety_score) / sd_safety_score
Zscore_safety_score

[1] 3.269324

FREQUENCY TABLE, BAR PLOT, AND HISTOGRAM

safety_score_frequency_table = table(safety_score_train)
safety_score_frequency_table

safety_score_train
 6 11 19 20 22 23 25 26 27 28 29 31 32 33 35 36 37 38 41 42 43 44 45 46 48 49 50 
 1  1  1  1  1  2  2  1  1  3  2  2  3  1  3  1  1  2  1  2  2  4  2  3  3  3  2 
51 52 53 54 55 56 57 58 59 60 61 64 65 66 67 68 70 73 74 75 76 77 78 83 86 87 92 
 2  2  2  3  1  2  1  3  2  3  3  2  1  1  1  1  1  1  1  2  1  1  2  1  1  2  1 
99 
 5 

safety_score_frequency_barplot = barplot(safety_score_frequency_table)

safety_score_frequency_barplot

      [,1]
 [1,]  0.7
 [2,]  1.9
 [3,]  3.1
 [4,]  4.3
 [5,]  5.5
 [6,]  6.7
 [7,]  7.9
 [8,]  9.1
 [9,] 10.3
[10,] 11.5
[11,] 12.7
[12,] 13.9
[13,] 15.1
[14,] 16.3
[15,] 17.5
[16,] 18.7
[17,] 19.9
[18,] 21.1
[19,] 22.3
[20,] 23.5
[21,] 24.7
[22,] 25.9
[23,] 27.1
[24,] 28.3
[25,] 29.5
[26,] 30.7
[27,] 31.9
[28,] 33.1
[29,] 34.3
[30,] 35.5
[31,] 36.7
[32,] 37.9
[33,] 39.1
[34,] 40.3
[35,] 41.5
[36,] 42.7
[37,] 43.9
[38,] 45.1
[39,] 46.3
[40,] 47.5
[41,] 48.7
[42,] 49.9
[43,] 51.1
[44,] 52.3
[45,] 53.5
[46,] 54.7
[47,] 55.9
[48,] 57.1
[49,] 58.3
[50,] 59.5
[51,] 60.7
[52,] 61.9
[53,] 63.1
[54,] 64.3
[55,] 65.5

safety_score_histogram = hist(safety_score_train)

safety_score_histogram

$breaks
 [1]   0  10  20  30  40  50  60  70  80  90 100

$counts
 [1]  1  3 12 13 22 21 10  8  4  6

$density
 [1] 0.001 0.003 0.012 0.013 0.022 0.021 0.010 0.008 0.004 0.006

$mids
 [1]  5 15 25 35 45 55 65 75 85 95

$xname
[1] "safety_score_train"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

PLOT SAFETY SCORE VS. FAMILY INVOLVEMENT

plot(safety_score_train, family_involvement_score_train)

scatter.smooth(safety_score_train, family_involvement_score_train)

CORRELATION (Between safety score and family involvement)

cor(safety_score_train,family_involvement_score_train)

[1] 0.7144638

CORRELATION FOR ALL VARIABLES (cor between ISAT reading an ISAT math is highest)

cor(chicago_public_schools_train[, c(10,12,14,16,18,20,22,24,26,28,29,30,31,32,33,35,36)])

                         Safety.Score Family.Involvement.Score Environment.Score
Safety.Score              1.000000000               0.71446375         0.6331058
Family.Involvement.Score  0.714463752               1.00000000         0.5347450
Environment.Score         0.633105824               0.53474498         1.0000000
Instruction.Score         0.476736067               0.42281132         0.8021495
Leaders.Score             0.450972507               0.68753901         0.3111567
Teachers.Score            0.483625772               0.72024487         0.3857252
Parent.Engagement.Score   0.592748544               0.54837537         0.4628990
Parent.Environment.Score  0.142646323               0.09603933         0.2465991
Rate.of.Misconducts      -0.495669900              -0.43192336        -0.3371369
ISAT.Exceeding.Math       0.712572291               0.61804691         0.4467668
ISAT.Exceeding.Reading    0.726116154               0.63542520         0.4461274
College.Enrollment        0.009967808               0.07970977        -0.1561447
Latitude                  0.356703198               0.24808717         0.2408997
Longitude                -0.268029157              -0.23382757        -0.1810229
Community.Area.Number    -0.333390485              -0.22394833        -0.2203719
Ward                      0.233385546               0.21651341         0.1368001
Police.District           0.341978820               0.31440629         0.2099816
                         Instruction.Score Leaders.Score Teachers.Score
Safety.Score                    0.47673607   0.450972507     0.48362577
Family.Involvement.Score        0.42281132   0.687539014     0.72024487
Environment.Score               0.80214954   0.311156740     0.38572521
Instruction.Score               1.00000000   0.275612091     0.36928230
Leaders.Score                   0.27561209   1.000000000     0.84169946
Teachers.Score                  0.36928230   0.841699464     1.00000000
Parent.Engagement.Score         0.35134311   0.367960680     0.36580246
Parent.Environment.Score        0.17761525   0.186121281     0.17695283
Rate.of.Misconducts            -0.31390321  -0.292251074    -0.33635458
ISAT.Exceeding.Math             0.42562395   0.354367646     0.40654925
ISAT.Exceeding.Reading          0.42144369   0.347355779     0.38259880
College.Enrollment             -0.13517904   0.065591651     0.08089638
Latitude                        0.08053262   0.051394903     0.10137811
Longitude                      -0.11812292  -0.117790806    -0.17495661
Community.Area.Number          -0.09394514   0.003562534    -0.06463487
Ward                            0.05829859  -0.046955755    -0.02924497
Police.District                 0.14048120   0.084473084     0.13792510
                         Parent.Engagement.Score Parent.Environment.Score
Safety.Score                          0.59274854              0.142646323
Family.Involvement.Score              0.54837537              0.096039333
Environment.Score                     0.46289904              0.246599115
Instruction.Score                     0.35134311              0.177615250
Leaders.Score                         0.36796068              0.186121281
Teachers.Score                        0.36580246              0.176952832
Parent.Engagement.Score               1.00000000              0.416902232
Parent.Environment.Score              0.41690223              1.000000000
Rate.of.Misconducts                  -0.25821245             -0.045287557
ISAT.Exceeding.Math                   0.52707099             -0.033321734
ISAT.Exceeding.Reading                0.57619786              0.002284523
College.Enrollment                   -0.09338198             -0.041730969
Latitude                              0.14905577              0.229623945
Longitude                            -0.29037015             -0.135261846
Community.Area.Number                -0.15761104             -0.177620170
Ward                                  0.21690821              0.195830879
Police.District                       0.29428698              0.285486204
                         Rate.of.Misconducts ISAT.Exceeding.Math
Safety.Score                     -0.49566990          0.71257229
Family.Involvement.Score         -0.43192336          0.61804691
Environment.Score                -0.33713693          0.44676682
Instruction.Score                -0.31390321          0.42562395
Leaders.Score                    -0.29225107          0.35436765
Teachers.Score                   -0.33635458          0.40654925
Parent.Engagement.Score          -0.25821245          0.52707099
Parent.Environment.Score         -0.04528756         -0.03332173
Rate.of.Misconducts               1.00000000         -0.40693328
ISAT.Exceeding.Math              -0.40693328          1.00000000
ISAT.Exceeding.Reading           -0.35054403          0.94774090
College.Enrollment               -0.10993665         -0.06453246
Latitude                         -0.23734628          0.18993892
Longitude                         0.16531982         -0.17766164
Community.Area.Number             0.19383470         -0.20739282
Ward                             -0.16714201          0.21848234
Police.District                  -0.26605091          0.26992417
                         ISAT.Exceeding.Reading College.Enrollment    Latitude
Safety.Score                        0.726116154        0.009967808  0.35670320
Family.Involvement.Score            0.635425201        0.079709769  0.24808717
Environment.Score                   0.446127381       -0.156144721  0.24089974
Instruction.Score                   0.421443690       -0.135179042  0.08053262
Leaders.Score                       0.347355779        0.065591651  0.05139490
Teachers.Score                      0.382598805        0.080896380  0.10137811
Parent.Engagement.Score             0.576197862       -0.093381983  0.14905577
Parent.Environment.Score            0.002284523       -0.041730969  0.22962394
Rate.of.Misconducts                -0.350544029       -0.109936648 -0.23734628
ISAT.Exceeding.Math                 0.947740900       -0.064532464  0.18993892
ISAT.Exceeding.Reading              1.000000000       -0.091278184  0.14306352
College.Enrollment                 -0.091278184        1.000000000  0.10148654
Latitude                            0.143063516        0.101486543  1.00000000
Longitude                          -0.124845355       -0.202645192 -0.55146576
Community.Area.Number              -0.192982956        0.046068177 -0.82238553
Ward                                0.213716652        0.090032088  0.63631360
Police.District                     0.261136018        0.066708299  0.55592915
                          Longitude Community.Area.Number        Ward
Safety.Score             -0.2680292          -0.333390485  0.23338555
Family.Involvement.Score -0.2338276          -0.223948325  0.21651341
Environment.Score        -0.1810229          -0.220371883  0.13680006
Instruction.Score        -0.1181229          -0.093945137  0.05829859
Leaders.Score            -0.1177908           0.003562534 -0.04695575
Teachers.Score           -0.1749566          -0.064634873 -0.02924497
Parent.Engagement.Score  -0.2903701          -0.157611037  0.21690821
Parent.Environment.Score -0.1352618          -0.177620170  0.19583088
Rate.of.Misconducts       0.1653198           0.193834695 -0.16714201
ISAT.Exceeding.Math      -0.1776616          -0.207392816  0.21848234
ISAT.Exceeding.Reading   -0.1248454          -0.192982956  0.21371665
College.Enrollment       -0.2026452           0.046068177  0.09003209
Latitude                 -0.5514658          -0.822385531  0.63631360
Longitude                 1.0000000           0.292572616 -0.46982444
Community.Area.Number     0.2925726           1.000000000 -0.51125531
Ward                     -0.4698244          -0.511255309  1.00000000
Police.District          -0.5188634          -0.437746322  0.71629262
                         Police.District
Safety.Score                  0.34197882
Family.Involvement.Score      0.31440629
Environment.Score             0.20998162
Instruction.Score             0.14048120
Leaders.Score                 0.08447308
Teachers.Score                0.13792510
Parent.Engagement.Score       0.29428698
Parent.Environment.Score      0.28548620
Rate.of.Misconducts          -0.26605091
ISAT.Exceeding.Math           0.26992417
ISAT.Exceeding.Reading        0.26113602
College.Enrollment            0.06670830
Latitude                      0.55592915
Longitude                    -0.51886345
Community.Area.Number        -0.43774632
Ward                          0.71629262
Police.District               1.00000000

SIMPLE LINEAR REGRESSION (Between safety_score and family_involvement_score) safety score predicted = 11.59217 + 0.78135*family involvement score

linear_reg = lm(safety_score_train ~ family_involvement_score_train)
summary(linear_reg)

Call:
lm(formula = safety_score_train ~ family_involvement_score_train)

Residuals:
    Min      1Q  Median      3Q     Max 
-32.627  -8.840  -0.925   8.741  61.623 

Coefficients:
                               Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    11.59217    4.23345   2.738  0.00734 ** 
family_involvement_score_train  0.78135    0.07729  10.109  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.68 on 98 degrees of freedom
Multiple R-squared:  0.5105,    Adjusted R-squared:  0.5055 
F-statistic: 102.2 on 1 and 98 DF,  p-value: < 2.2e-16

PREDICTED VALUES USING SIMPLE LINEAR REGRESSION (Assume fam involvement = 90)

safety_score_predicted_LR = 11.59217 + 0.78135*90
safety_score_predicted_LR

[1] 81.91367

PLOTTING WITH A TREND LINE

plot(safety_score_train,family_involvement_score_train)
abline(reg, col="blue", lwd=2)

only using the first two of 3 regression coefficients

MULTIPLE LINEAR REGRESSION safety score = 0.47290 + 0.57574fam involvement + 0.42421environment score

multiple_linear_regression= lm(safety_score_train ~ family_involvement_score_train + environment_score_train)
summary(multiple_linear_regression)

Call:
lm(formula = safety_score_train ~ family_involvement_score_train + 
    environment_score_train)

Residuals:
    Min      1Q  Median      3Q     Max 
-27.318  -7.387  -0.214   9.256  51.530 

Coefficients:
                               Estimate Std. Error t value Pr(>|t|)    
(Intercept)                     0.47290    4.54278   0.104    0.917    
family_involvement_score_train  0.57574    0.08324   6.917 4.96e-10 ***
environment_score_train         0.42421    0.09184   4.619 1.18e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.36 on 97 degrees of freedom
Multiple R-squared:  0.5987,    Adjusted R-squared:  0.5905 
F-statistic: 72.36 on 2 and 97 DF,  p-value: < 2.2e-16

problem_9_regression_1 = lm(ISAT_exceeding_math_train ~ safety_score_train + parent_environment_score_train)
summary(problem_9_regression_1)

Call:
lm(formula = ISAT_exceeding_math_train ~ safety_score_train + 
    parent_environment_score_train)

Residuals:
    Min      1Q  Median      3Q     Max 
-23.032  -7.241  -1.196   5.276  47.839 

Coefficients:
                               Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    18.40039   14.27842   1.289   0.2006    
safety_score_train              0.60722    0.05855  10.371   <2e-16 ***
parent_environment_score_train -0.55923    0.28658  -1.951   0.0539 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12.04 on 97 degrees of freedom
Multiple R-squared:  0.5264,    Adjusted R-squared:  0.5166 
F-statistic:  53.9 on 2 and 97 DF,  p-value: < 2.2e-16

score_predict_final = coef(problem_9_regression_1)[1] + coef(problem_9_regression_1)[2] + coef(problem_9_regression_1)[3]

problem_9_regression_2 = lm(ISAT_exceeding_math_train ~ rate_of_misconduct_train + teachers_score_train)
summary(problem_9_regression_2)

Call:
lm(formula = ISAT_exceeding_math_train ~ rate_of_misconduct_train + 
    teachers_score_train)

Residuals:
    Min      1Q  Median      3Q     Max 
-22.319  -8.709  -2.169   3.127  58.882 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)   
(Intercept)              11.83466    5.33293   2.219  0.02881 * 
rate_of_misconduct_train -0.25621    0.07865  -3.258  0.00155 **
teachers_score_train      0.28462    0.08754   3.251  0.00158 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.18 on 97 degrees of freedom
Multiple R-squared:  0.2476,    Adjusted R-squared:  0.2321 
F-statistic: 15.96 on 2 and 97 DF,  p-value: 1.018e-06

PREDICTING VALUES USING MULTIPLE LINEAR REGRESSION (Assume fam involvement = 90 and environment = 80)

safety_score_predicted_MLR = 0.47290 + 0.57574*90 + 0.42421*80
safety_score_predicted_MLR

[1] 86.2263

LINEAR MODEL VS. ACTUAL DATA

plot(safety_score_train,family_involvement_score_train)
abline(linear_reg, col="blue", lwd=2)

QUADRATIC MODEL

family_involvement_score_train2 = family_involvement_score_train^2
quad_model = lm(safety_score_train ~ family_involvement_score_train +family_involvement_score_train2)
summary(quad_model)

Call:
lm(formula = safety_score_train ~ family_involvement_score_train + 
    family_involvement_score_train2)

Residuals:
    Min      1Q  Median      3Q     Max 
-32.158  -9.109  -0.833   7.946  60.800 

Coefficients:
                                 Estimate Std. Error t value Pr(>|t|)  
(Intercept)                     23.018349   9.959782   2.311   0.0229 *
family_involvement_score_train   0.331606   0.363352   0.913   0.3637  
family_involvement_score_train2  0.003893   0.003073   1.267   0.2083  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.64 on 97 degrees of freedom
Multiple R-squared:  0.5184,    Adjusted R-squared:  0.5085 
F-statistic: 52.21 on 2 and 97 DF,  p-value: 4.067e-16

PREDICT USING QUADRATIC MODEL (When x=1)

safety_score_predicted_QM = 23.018349 + 0.331606*1 + 0.003893*1^2
safety_score_predicted_QM

[1] 23.35385

PLOTTING QUADRATIC MODEL VS. LINEAR

safety_score_predicted_QM = predict(quad_model,data=chicago_public_schools_train)
plot(safety_score_predicted_QM, col="red", pch=16)

plot(safety_score_train,family_involvement_score_train, pch=16)

CUBIC MODEL

family_involvement_score_train3 = family_involvement_score_train^3
cubic_model = lm(safety_score_train ~ family_involvement_score_train + family_involvement_score_train2 + family_involvement_score_train3)
summary(cubic_model)

Call:
lm(formula = safety_score_train ~ family_involvement_score_train + 
    family_involvement_score_train2 + family_involvement_score_train3)

Residuals:
    Min      1Q  Median      3Q     Max 
-31.819  -9.375  -0.920   7.808  61.020 

Coefficients:
                                  Estimate Std. Error t value Pr(>|t|)
(Intercept)                      2.855e+01  2.370e+01   1.205    0.231
family_involvement_score_train  -2.293e-02  1.424e+00  -0.016    0.987
family_involvement_score_train2  1.061e-02  2.628e-02   0.404    0.687
family_involvement_score_train3 -3.822e-05  1.484e-04  -0.258    0.797

Residual standard error: 14.71 on 96 degrees of freedom
Multiple R-squared:  0.5188,    Adjusted R-squared:  0.5037 
F-statistic: 34.49 on 3 and 96 DF,  p-value: 3.247e-15

PREDICT USING CUBIC MODEL

safety_score_predicted_CM = predict(cubic_model,data=chicago_public_schools_train)

PLOT CUBIC MODEL VS. LINEAR

plot(safety_score_train,family_involvement_score_train, pch=16)

plot(safety_score_predicted_CM, col="green", pch=16)

score_predict_final = 18.40039 + 0.60722* safety_score_train +