R Notebook

powerball_data = read.csv(file = "Powerball csv.csv")
head(powerball_data)

first_number = powerball_data$First.number
second_number = powerball_data$Second.Number
third_number = powerball_data$Third.Number
fourth_number = powerball_data$Fourth.Number
fifth_number = powerball_data$Fifth.Number

summary(powerball_data)

             Draw.Date       Order         First.number   Second.Number  
 Sat, Apr 01, 2017:  1   Min.   :  1.00   Min.   : 1.00   Min.   : 2.00  
 Sat, Apr 07, 2018:  1   1st Qu.: 54.75   1st Qu.: 5.00   1st Qu.:14.75  
 Sat, Apr 08, 2017:  1   Median :108.50   Median :10.00   Median :22.00  
 Sat, Apr 14, 2018:  1   Mean   :108.50   Mean   :12.41   Mean   :24.07  
 Sat, Apr 15, 2017:  1   3rd Qu.:162.25   3rd Qu.:18.25   3rd Qu.:32.00  
 Sat, Apr 21, 2018:  1   Max.   :216.00   Max.   :50.00   Max.   :61.00  
 (Other)          :210                                                   
  Third.Number   Fourth.Number    Fifth.Number         PB       
 Min.   : 7.00   Min.   :15.00   Min.   :23.00   Min.   : 1.00  
 1st Qu.:27.00   1st Qu.:40.00   1st Qu.:53.00   1st Qu.: 8.00  
 Median :36.00   Median :48.00   Median :61.00   Median :14.00  
 Mean   :36.12   Mean   :47.04   Mean   :58.24   Mean   :13.98  
 3rd Qu.:45.00   3rd Qu.:57.00   3rd Qu.:66.00   3rd Qu.:21.00  
 Max.   :64.00   Max.   :68.00   Max.   :69.00   Max.   :26.00  
                                                                
   Power.Play                Jackpot   
 Min.   : 2.000   $40.00 Million : 15  
 1st Qu.: 2.000   $50.00 Million :  8  
 Median : 2.000   $60.00 Million :  7  
 Mean   : 2.644   $80.00 Million :  6  
 3rd Qu.: 3.000   $70.00 Million :  5  
 Max.   :10.000   $100.00 Million:  4  
                  (Other)        :171  

FIRST NUMBER POSSIBILITIES = 1-50 SECOND NUMBER POSSIBILITIES = 2-61 THIRD NUMBER POSSIBILITIES = 7-64 FOURTH NUMBER POSSIBILITIES = 15-68 FIFTH NUMBER POSSIBILITIES = 23-69

scatter.smooth(first_number)

scatter.smooth(second_number)

scatter.smooth(third_number)

scatter.smooth(fourth_number)

scatter.smooth(fifth_number)

cor(powerball_data[,c(2,3,4,5,6,7,8,9)])

                     Order First.number Second.Number Third.Number
Order          1.000000000   0.00749623  -0.048474909  -0.04517491
First.number   0.007496230   1.00000000   0.617934431   0.43950464
Second.Number -0.048474909   0.61793443   1.000000000   0.75508139
Third.Number  -0.045174912   0.43950464   0.755081390   1.00000000
Fourth.Number -0.075205377   0.37593956   0.585785958   0.78539574
Fifth.Number  -0.002441859   0.26564158   0.388036157   0.54681435
PB            -0.077599905  -0.10191896  -0.099358907  -0.09597954
Power.Play    -0.085907116   0.05171796   0.006389309  -0.03959939
              Fourth.Number  Fifth.Number          PB    Power.Play
Order           -0.07520538 -0.0024418593 -0.07759990 -0.0859071163
First.number     0.37593956  0.2656415832 -0.10191896  0.0517179581
Second.Number    0.58578596  0.3880361574 -0.09935891  0.0063893095
Third.Number     0.78539574  0.5468143474 -0.09597954 -0.0395993926
Fourth.Number    1.00000000  0.6667634848 -0.09822327  0.0454489285
Fifth.Number     0.66676348  1.0000000000 -0.02900352 -0.0007800508
PB              -0.09822327 -0.0290035166  1.00000000 -0.0433355184
Power.Play       0.04544893 -0.0007800508 -0.04333552  1.0000000000

HIGHEST TO LOWEST CORRELATIONS THIRD NUMBER - FOURTH NUMBER 0.785 SECOND NUMBER - THIRD NUMBER 0.755 FOURTH NUMBER - FIFTH NUMBER 0.667 FIRST NUMBER - SECOND NUMBER 0.618 SECOND NUMBER - FOURTH NUMBER 0.586

linear_regression_34 = lm(third_number ~ fourth_number)
summary(linear_regression_34)

Call:
lm(formula = third_number ~ fourth_number)

Residuals:
    Min      1Q  Median      3Q     Max 
-27.810  -5.201   2.406   6.341  12.330 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -4.2077     2.2477  -1.872   0.0626 .  
fourth_number   0.8575     0.0462  18.561   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.447 on 214 degrees of freedom
Multiple R-squared:  0.6168,    Adjusted R-squared:  0.6151 
F-statistic: 344.5 on 1 and 214 DF,  p-value: < 2.2e-16

THIRD NUMBER PREDICTED = -4.2077 + 0.8575(FOURTH NUMBER)

linear_regression_23 = lm(second_number ~ third_number)
summary(linear_regression_23)

Call:
lm(formula = second_number ~ third_number)

Residuals:
     Min       1Q   Median       3Q      Max 
-27.8911  -5.4014   0.8112   5.8854  17.6760 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.81231    1.64123  -1.104    0.271    
third_number  0.71645    0.04253  16.848   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.489 on 214 degrees of freedom
Multiple R-squared:  0.5701,    Adjusted R-squared:  0.5681 
F-statistic: 283.8 on 1 and 214 DF,  p-value: < 2.2e-16

SECOND NUMBER PREDICTED = -1.81231 + 0.71645(THHIRD NUMBER)

linear_regression_45 = lm(fourth_number ~ fifth_number)
summary(linear_regression_45)

Call:
lm(formula = fourth_number ~ fifth_number)

Residuals:
    Min      1Q  Median      3Q     Max 
-37.031  -6.069   2.811   7.479  11.969 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.62521    3.77179  -0.431    0.667    
fifth_number  0.83560    0.06385  13.088   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.316 on 214 degrees of freedom
Multiple R-squared:  0.4446,    Adjusted R-squared:  0.442 
F-statistic: 171.3 on 1 and 214 DF,  p-value: < 2.2e-16

FOURTH NUMBER PREDICTED = -1.62521 + 0.83560(FIFTH NUMBER)

linear_regression_12 = lm(first_number ~ second_number)
summary(linear_regression_12)

Call:
lm(formula = first_number ~ second_number)

Residuals:
     Min       1Q   Median       3Q      Max 
-24.8391  -4.7736  -0.3344   5.0214  24.9717 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)    1.13613    1.11249   1.021    0.308    
second_number  0.46847    0.04075  11.497   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.718 on 214 degrees of freedom
Multiple R-squared:  0.3818,    Adjusted R-squared:  0.379 
F-statistic: 132.2 on 1 and 214 DF,  p-value: < 2.2e-16

**FIRST NUMBER PREDICTED = 1.12613 + 0.46847(SECOND NUMBER)

linear_regression_24 = lm(second_number ~ fourth_number)
summary(linear_regression_24)

Call:
lm(formula = second_number ~ fourth_number)

Residuals:
    Min      1Q  Median      3Q     Max 
-27.115  -7.507  -1.132   7.363  26.637 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -4.47356    2.79237  -1.602    0.111    
fourth_number  0.60682    0.05739  10.573   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.49 on 214 degrees of freedom
Multiple R-squared:  0.3431,    Adjusted R-squared:  0.3401 
F-statistic: 111.8 on 1 and 214 DF,  p-value: < 2.2e-16