# Stat Project

9 September 2016

In order to figure out how variables relates to each other and the connections among the variables, or one can predict the other. I will choose three quantitative variables or two quantitative variables and one categorical variable on each pairs. I will also use graphs of scatter plots; regression and correlation to understand that how one variable affect other two variables.

There are six groups below: Group one: High School Percentile (HSP), Cumulative GPA (GPA), and ACT Composition Score (COMP) a) HSP vs GPA b) HSP vs COMP c) COMP vs GPA From graph a, we can find out that there is moderate positive liner relationship between HSP and GPA; the correlation is 0. 552; the equation of regression is GPA=0. 0163928*HSP+1. 84804; the slope is 0. 0163928 which is positive; when the predictor variable HSP increase, the response variable GPA also moderately increase; for instance, when HSP increase by 1, GPA will increase 0. 0163928.

## Stat Project Essay Example

From graph b, there is also weak positive liner relationship between HSP and COMP scores; the correlation is 0. 357; the equation of regression is COMP=0. 069129*HSP+18. 3131; the slope is 0. 069129 which is positive; when the predictor variable HSP increase, the response variable COMP scores also weakly increase; for example, when HSP increase by 1, the COMP scores will increase 0. 069129. From graph c, there is another weak positive liner relationship between COMP scores and GPA; the correlation is 0. 342; the equation of regression is GPA=0. 0524047*COMP+1. 243; the slope is 0. 0524047 which is positive; when the predictor variable COMP increase, the response variable GPA also weakly increase; for example, COMP scores increase by 1, the GPA will increase 0. 0524047.

Based on the graphs and data which I got, I think there are only a little relation among HSP, COMP scores and GPA. I can find out a student with high HSP, has high GPA and high COMP scores; the student with high COMP scores has high GPA. Group Two: ACT math score (MATH), ACT English score (ENGLISH) and Cumulative GPA (GPA) a) MATH vs GPA ) ENGLISH vs GPA c) ENGLISH vs MATH From graph a, we can see that there is weak positive liner relationship between MATH scores and GPA; the correlation is 0. 307; the equation of regression is GPA=0. 0395427*MATH+2. 12892; the slope is 0. 0395427 which is positive; when the predictor variable MATH scores increase, the response variable GPA also weakly increase; for instance, when MATH increase by 1, GPA will increase 0. 0395427. From graph b, there is also weak positive liner relationship between ENGLISH scores and GPA; the correlation is 0. 45; the equation of regression is GPA=0. 0411408*ENGLISH+2. 11295; the slope is 0. 0411408 which is positive; when the predictor variable ENGLISH scores increase, the response variable GPA also weakly increase; for example, when ENGLISH scores increase by 1, the GPA will increase 0. 0411408.

From graph c, there is moderate positive liner relationship between ENGLISH scores and MATH scores; the correlation is 0. 475; the equation of regression is MATH=0. 440334*ENGLISH+13. 2567; the slope is 0. 40334 which is positive; when the predictor variable ENGLISH scores increase, the response variable MATH scores also weakly increase; for instance, when ENGLISH scores increase by 1, the MATH scores will increase 0. 440334. According to the graphs and data, I can find out a student who has high English score and Math score also has high GPA and the student with high English score has high Math score. Group Three: Cumulative GPA (GPA), age (AGE) and Total Credits Earned (CREDITS) a) AGE vs GPA b) CREDITS vs GPA c) AGE vs CREDITS

From graph a, we can see that there is a weak negative liner relationship between AGE and GPA; the correlation is -0. 103; the equation of regression is GPA=-0. 0240245*AGE+3. 55195; the slope is -0. 0240245 which is negative; when the predictor variable AGE increase, the response variable GPA will weakly decrease; for instance, when AGE increase by 1, GPA will decrease 0. 0240245. From graph b, there is weak positive liner relationship between CREDITS and GPA; the correlation is 0. 106; the equation of regression is GPA=0. 00141886*CREDITS+2. 94831; the slope is 0. 0141886 which is positive; when the predictor variable CREDITS increase, the response variable GPA also weakly increase; for example, when CREDITS increase by 1, the GPA will increase 0. 00141886. From graph c, there is a strong positive liner association between AGE and CREDITS; the correlation is 0. 668; the equation of regression is CREDITS=11. 7475*AGE-174. 356; the slope is 11. 7475 which is positive; when the predictor variable AGE increase, the response variable CREDITS also strongly increase; for instance, when AGE increase by 1, the CREDITS will increase 11. 7475.

There are some outliers may affect the correlation. Based on the graphs and data above, we can find out a student who is older with a litter lower GPA, but has very higher credits; the student with higher credits also has high GPA. Group Four: ACT English Score (ENGLISH), ACT Composition Score (COMP) and Age (AGE) a) AGE vs ENGLISH b) AGE vs COMP c) ENGLISH vs COMP From graph a, we can see that there is a weak negative liner relationship between AGE and English scores; the correlation is -0. 042; the equation of regression is ENGLISH=-0. 0814809*AGE+24. 469; the slope is -0. 814809 which is negative; when the predictor variable AGE increase, the response variable English scores will weakly decrease; for instance, when AGE increase by 1, GPA will decrease 0. 0814809. From graph b, there is weak negative liner relationship between ENGLISH scores and COMP scores; the correlation is-0. 038; the equation of regression is COMP=-0. 0584814*AGE+24. 6029; the slope is -0. 0584814 which is negative; when the predictor variable CREDITS increase, the response variable GPA also weakly increase; for example, when AGE increase by 1, the COMP scores will decrease 0. 0584814.

From graph c, there is a strong positive liner association between ENGLISH scores and COMP scores; the correlation is 0. 843; the equation of regression is COMP=0. 65656*ENGLISH+8. 43327; the slope is 0. 65656 which is positive; when the predictor variable ENGLISH scores increase, the response variable COMP scores also strongly increase; for instance, when ENGLISH scores increase by 1, the COMP scores will increase 0. 65656. According to the graphs and data above, we can find out a student who is older with a litter lower English and Comp scores; the student with higher English score has very high Comp score.

Group Five: Quantitative variables High School Percentile (HSP), Age (AGE) and a categorical variable Sex (SEX) a) HSP vs GPA (both sex) b) HSP vs GPA (males) c) HSP vs GPA (females) From graph a, we can see that there is a moderate positive liner relationship between HSP and GPA; the correlation is 0. 552; the equation of regression is GPA=0. 0163928*HSP+1. 8408; the slope is 0. 0163928 which is positive; when the predictor variable HSP increase, the response variable GPA will moderate increase.

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