1. Estimate and interpret a regression model for college GPA (for enrolled students, university-wide), based on the predictor of HS GPA. Develop another model based on the predictor of SAT score. Finally, develop another model combining these two predictors into a single model. Use k-fold cross-validation to select the best predictive model, with k=4.

Include your model output on a spreadsheet tab labelled Regression.

Summarize your findings in the Word document. Which (if any) model would you recommend for predicting college academic success, and why? Are there any violations of model assumptions associated with any of these models?

Master Data High School GPA SAT/ACT Education_Parenti Education_Parent2 College_GPA Mean Mean 1164.58158 Mean 5.11903801 Mean 5.03281619 Mean 3.08328534 Standard Error 3.55593287 0.00351252 3.59 0.01375915 0.01309318 0.01313693 Standard Error Median 1.30934637 1170 Standard Error Median Standard Error Median Standard Error Median 6 6 3.1395 4 Mode 1170 Mode 6 Mode 3.028 Mode Standard Deviation 1.72407929 0.46252086 0.21392555 0.51351778 6 1.8117722 3.28251849 Standard Deviation Sample Variance Kurtosis 172.411636 29725.7723 0.01579165 Sample Variance Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Standard Deviation Sample Variance Kurtosis 2.97244939 Standard Deviation Sample Variance Kurtosis 0.26370051 2.02769748 Kurtosis -0.57149915 -0.46575894 2.29282999 -0.72896787 Skewness Skewness -0.76074925 Skewness -0.73207436 -1.08559481 -0.2326674 1320 Skewness Range 4.5 Range 6 6 Range Minimum 3.636 0.364 0 Minimum Range Minimum Maximum 280 1 1 Minimum Maximum 4.5 7 Maximum 7 4 Maximum Sum Sum 61656.32 1600 20192680 17339 Sum 88759 Sum 4711.26 Sum Count 87264 17339 Count 17339 Count Count 17339 Count 1528 College 1 High School GPA SAT/ACT Education_Parent1 Education_Parent2 College GPA Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.49785468 0.00546811 3.53 3.5 0.45631685 0.20822507 1.10816587 -0.53127653 4.5 0 4.5 24359.06 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1146.35698 2.04116076 1150 1170 170.336058 29014.3726 0.1376296 -0.28788574 1310 280 1590 7983230 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.11875359 0.02166156 6 6 1.80766995 3.26767066 -0.55393027 -0.76639916 6 1 7 35647 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.07926479 0.02065244 6 6 1.72345779 2.97030674 -0.40791099 -0.76143643 6 1 7 35372 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.17592606 0.02042108 3.242 3.584 0.47498225 0.22560814 2.08047747 -1.05875062 3.111 0.889 1718.176 541 College 2 High School GPA SAT/ACT Education Parent1 Education_Parent2 College_GPA 5.09675847 0.02563079 6 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.53824031 0.00718006 3.59 3.5 0.45991602 0.21152274 2.93209747 -0.86350166 4.42 0 4.42 14517.4 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1173.63149 2.62167723 1180 1210 167.930655 28200.7047 0.01597572 -0.23621838 1200 390 1590 4815410 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.26224714 0.02690563 6 6 1.72343118 2.97021504 -0.28196106 -0.89183088 6 1 7 21591 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 6 1.6417715 2.69541367 -0.2959923 -0.79676686 6 1 7 20912 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.04201202 0.02188933 3.09 3.344 0.48897059 0.23909224 2.90491252 -1.12605706 3.595 0.364 3.959 1517.964 499 College 3 High School GPA SAT/ACT Education_Parent1 Education_Parent2 College GPA 3.63199298 0.00581604 3.68 4 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 0.46060648 0.21215833 2.84399914 -0.91555217 4.5 0 4.5 22779.86 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1178.89668 2.21944079 1180 1190 175.770743 30895.354 -0.14172393 -0.19317121 1240 360 1600 7394040 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.02566964 0.02356263 6 6 1.86606499 3.48219856 -0.74564887 -0.67038312 6 1 7 31521 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 4.93941327 0.02238632 6 6 1.77290586 3.14319519 -0.62565554 -0.65625363 6 1 7 30980 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.02278689 0.02549665 3.0875 3.028 0.56323934 0.31723855 1.8274721 -1.0294115 3.283 0.717 4 1475.12 488 Race Master Collere 1 College 2 College White Asian Other Count 9165 3004 5170 17339 3871 856 2237 6964 2218 822 1063 4103 3076 1317 1879 6272 Master Data High School GPA SAT/ACT Education_Parenti Education_Parent2 College_GPA Mean Mean 1164.58158 Mean 5.11903801 Mean 5.03281619 Mean 3.08328534 Standard Error 3.55593287 0.00351252 3.59 0.01375915 0.01309318 0.01313693 Standard Error Median 1.30934637 1170 Standard Error Median Standard Error Median Standard Error Median 6 6 3.1395 4 Mode 1170 Mode 6 Mode 3.028 Mode Standard Deviation 1.72407929 0.46252086 0.21392555 0.51351778 6 1.8117722 3.28251849 Standard Deviation Sample Variance Kurtosis 172.411636 29725.7723 0.01579165 Sample Variance Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Standard Deviation Sample Variance Kurtosis 2.97244939 Standard Deviation Sample Variance Kurtosis 0.26370051 2.02769748 Kurtosis -0.57149915 -0.46575894 2.29282999 -0.72896787 Skewness Skewness -0.76074925 Skewness -0.73207436 -1.08559481 -0.2326674 1320 Skewness Range 4.5 Range 6 6 Range Minimum 3.636 0.364 0 Minimum Range Minimum Maximum 280 1 1 Minimum Maximum 4.5 7 Maximum 7 4 Maximum Sum Sum 61656.32 1600 20192680 17339 Sum 88759 Sum 4711.26 Sum Count 87264 17339 Count 17339 Count Count 17339 Count 1528 College 1 High School GPA SAT/ACT Education_Parent1 Education_Parent2 College GPA Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.49785468 0.00546811 3.53 3.5 0.45631685 0.20822507 1.10816587 -0.53127653 4.5 0 4.5 24359.06 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1146.35698 2.04116076 1150 1170 170.336058 29014.3726 0.1376296 -0.28788574 1310 280 1590 7983230 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.11875359 0.02166156 6 6 1.80766995 3.26767066 -0.55393027 -0.76639916 6 1 7 35647 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.07926479 0.02065244 6 6 1.72345779 2.97030674 -0.40791099 -0.76143643 6 1 7 35372 6964 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.17592606 0.02042108 3.242 3.584 0.47498225 0.22560814 2.08047747 -1.05875062 3.111 0.889 1718.176 541 College 2 High School GPA SAT/ACT Education Parent1 Education_Parent2 College_GPA 5.09675847 0.02563079 6 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.53824031 0.00718006 3.59 3.5 0.45991602 0.21152274 2.93209747 -0.86350166 4.42 0 4.42 14517.4 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1173.63149 2.62167723 1180 1210 167.930655 28200.7047 0.01597572 -0.23621838 1200 390 1590 4815410 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.26224714 0.02690563 6 6 1.72343118 2.97021504 -0.28196106 -0.89183088 6 1 7 21591 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 6 1.6417715 2.69541367 -0.2959923 -0.79676686 6 1 7 20912 4103 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.04201202 0.02188933 3.09 3.344 0.48897059 0.23909224 2.90491252 -1.12605706 3.595 0.364 3.959 1517.964 499 College 3 High School GPA SAT/ACT Education_Parent1 Education_Parent2 College GPA 3.63199298 0.00581604 3.68 4 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 0.46060648 0.21215833 2.84399914 -0.91555217 4.5 0 4.5 22779.86 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1178.89668 2.21944079 1180 1190 175.770743 30895.354 -0.14172393 -0.19317121 1240 360 1600 7394040 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 5.02566964 0.02356263 6 6 1.86606499 3.48219856 -0.74564887 -0.67038312 6 1 7 31521 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 4.93941327 0.02238632 6 6 1.77290586 3.14319519 -0.62565554 -0.65625363 6 1 7 30980 6272 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.02278689 0.02549665 3.0875 3.028 0.56323934 0.31723855 1.8274721 -1.0294115 3.283 0.717 4 1475.12 488 Race Master Collere 1 College 2 College White Asian Other Count 9165 3004 5170 17339 3871 856 2237 6964 2218 822 1063 4103 3076 1317 1879 6272