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Jupyter notebook NotWorking/run.ipynb

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Kernel: R (SageMath)
load(file="workspace2.rdata")

summary(fitcool2)
Call: lm(formula = cGPA ~ sleephrsday + I(sleephrsday^2) + studyhrsday + I(studyhrsday^2) + I(studyhrsday^3) + I(studyhrsday^4) + I(studyhrsday^5) + I(studyhrsday^6) + avgau + I(avgau^2) + I(avgau^3) + I(avgau^4) + targetmingpa + I(targetmingpa^2) + I(targetmingpa^3) + I(targetmingpa^4)) Residuals: Min 1Q Median 3Q Max -0.64111 -0.20894 0.06135 0.17735 0.72014 Coefficients: (1 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 7.595e+01 5.891e+01 1.289 0.2075 sleephrsday 8.370e-01 5.938e-01 1.410 0.1693 I(sleephrsday^2) -5.435e-02 4.798e-02 -1.133 0.2666 studyhrsday 5.205e+00 2.589e+00 2.010 0.0538 . I(studyhrsday^2) -2.201e+00 1.325e+00 -1.662 0.1073 I(studyhrsday^3) 4.712e-01 3.294e-01 1.431 0.1632 I(studyhrsday^4) -5.465e-02 4.221e-02 -1.295 0.2057 I(studyhrsday^5) 3.258e-03 2.669e-03 1.221 0.2320 I(studyhrsday^6) -7.776e-05 6.569e-05 -1.184 0.2461 avgau -4.143e+00 6.236e+00 -0.664 0.5117 I(avgau^2) 4.570e-01 5.818e-01 0.785 0.4386 I(avgau^3) -2.112e-02 2.358e-02 -0.896 0.3777 I(avgau^4) 3.482e-04 3.504e-04 0.994 0.3286 targetmingpa -5.523e+01 3.970e+01 -1.391 0.1748 I(targetmingpa^2) 1.464e+01 1.040e+01 1.408 0.1698 I(targetmingpa^3) -1.251e+00 9.013e-01 -1.388 0.1758 I(targetmingpa^4) NA NA NA NA --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.365 on 29 degrees of freedom Multiple R-squared: 0.8336, Adjusted R-squared: 0.7475 F-statistic: 9.683 on 15 and 29 DF, p-value: 1.388e-07 
predict(fitcool2, data.frame(sleephrsday=8,studyhrsday=6,avgau=9.8,targetmingpa=4.5),interval="confidence",level=0.75)
Warning message in predict.lm(fitcool2, data.frame(sleephrsday = 8, studyhrsday = 6, : “prediction from a rank-deficient fit may be misleading”
fit lwr upr 1 4.348646 3.948909 4.748382
fitcool3 = lm(cGPA~sleephrsday+I(sleephrsday^2)+studyhrsday+I(studyhrsday^2)+I(studyhrsday^3)+I(studyhrsday^4)+I(studyhrsday^5)+I(studyhrsday^6)+avgau+I(avgau^2)+I(avgau^3)+I(avgau^4)+motivate+I(motivate^2)+I(motivate^3)+targetmingpa+I(targetmingpa^2)+I(targetmingpa^3)+I(targetmingpa^4)+workhrsweek+I(workhrsweek^2)+I(workhrsweek^3)+I(workhrsweek^4))
summary(fitcool3)
Call: lm(formula = cGPA ~ sleephrsday + I(sleephrsday^2) + studyhrsday + I(studyhrsday^2) + I(studyhrsday^3) + I(studyhrsday^4) + I(studyhrsday^5) + I(studyhrsday^6) + avgau + I(avgau^2) + I(avgau^3) + I(avgau^4) + motivate + I(motivate^2) + I(motivate^3) + targetmingpa + I(targetmingpa^2) + I(targetmingpa^3) + I(targetmingpa^4) + workhrsweek + I(workhrsweek^2) + I(workhrsweek^3) + I(workhrsweek^4)) Residuals: Min 1Q Median 3Q Max -0.59536 -0.19057 0.06449 0.16885 0.69697 Coefficients: (5 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 9.549e+01 6.829e+01 1.398 0.174 sleephrsday 7.599e-01 6.432e-01 1.181 0.248 I(sleephrsday^2) -4.814e-02 5.167e-02 -0.932 0.360 studyhrsday 4.699e+00 2.902e+00 1.619 0.117 I(studyhrsday^2) -1.935e+00 1.496e+00 -1.294 0.207 I(studyhrsday^3) 4.080e-01 3.707e-01 1.101 0.281 I(studyhrsday^4) -4.703e-02 4.719e-02 -0.996 0.328 I(studyhrsday^5) 2.805e-03 2.963e-03 0.947 0.353 I(studyhrsday^6) -6.721e-05 7.251e-05 -0.927 0.363 avgau -4.565e+00 6.629e+00 -0.689 0.497 I(avgau^2) 4.962e-01 6.155e-01 0.806 0.427 I(avgau^3) -2.268e-02 2.485e-02 -0.913 0.370 I(avgau^4) 3.708e-04 3.682e-04 1.007 0.323 motivate -3.821e-01 1.329e+00 -0.288 0.776 I(motivate^2) 7.688e-02 4.611e-01 0.167 0.869 I(motivate^3) -4.194e-03 4.892e-02 -0.086 0.932 targetmingpa -6.864e+01 4.804e+01 -1.429 0.165 I(targetmingpa^2) 1.817e+01 1.262e+01 1.440 0.162 I(targetmingpa^3) -1.559e+00 1.097e+00 -1.421 0.167 I(targetmingpa^4) NA NA NA NA workhrsweek NA NA NA NA I(workhrsweek^2) NA NA NA NA I(workhrsweek^3) NA NA NA NA I(workhrsweek^4) NA NA NA NA Residual standard error: 0.3807 on 26 degrees of freedom Multiple R-squared: 0.8376, Adjusted R-squared: 0.7252 F-statistic: 7.452 on 18 and 26 DF, p-value: 3.015e-06 
predict(fitcool3, data.frame(sleephrsday=6,studyhrsday=5,avgau=17,motivate=3,targetmingpa=3,workhrsweek=0),interval="confidence",level=0.75)
Warning message in predict.lm(fitcool3, data.frame(sleephrsday = 6, studyhrsday = 5, : “prediction from a rank-deficient fit may be misleading”
fit lwr upr 1 3.029891 2.425224 3.634559
summary(cGPA)
Min. 1st Qu. Median Mean 3rd Qu. Max. 2.500 3.470 4.050 3.948 4.640 5.000 
summary(studyhrsday)
Min. 1st Qu. Median Mean 3rd Qu. Max. 1.000 4.000 5.000 5.711 8.000 13.000 
# Winston
# Introduce all to 3rd power => R = 0.94
# Realised motivate^3 is NA, therefore eliminate cubic term [other possibility: introduce quartic]
# Check behaviour (ordered terms according to most to least well understood extreme behaviour)
testdummy = lm(cGPA~
               sleephrsday
               +motivate
               +studyhrsday
               +avgau
              )
summary(testdummy)
Call: lm(formula = cGPA ~ sleephrsday + motivate + studyhrsday + avgau) Residuals: Min 1Q Median 3Q Max -1.3154 -0.5305 0.1240 0.4596 1.1184 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.62410 0.98470 1.649 0.1069 sleephrsday 0.24884 0.09549 2.606 0.0128 * motivate 0.02750 0.12165 0.226 0.8223 studyhrsday 0.02569 0.03591 0.715 0.4786 avgau 0.02890 0.03335 0.867 0.3913 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6928 on 40 degrees of freedom Multiple R-squared: 0.1727, Adjusted R-squared: 0.09 F-statistic: 2.088 on 4 and 40 DF, p-value: 0.1004