# explain multiple linear regression and the determinants associated with it

11/09/2019
###### Internal Environmental Analysis/Strategy Analysis And Strategy
11/09/2019

Professional Assignment 2

Please explain multiple linear regression and the determinants associated with it. Use the Excel file as the sample data which is suitable for multiple regression analysis (“Data” tab). Perform the regression modeling on the data (I already did it in “Regression” tab); and interpret your result. Evaluate the associated correlation coefficients and discuss if there is consistency between the correlations and the coefficients in the regression model. It is highly recommended that you look at the correlation matrix first to avoid situations in which there is excessively high correlation in either direction. You need to have at least two independent variables in your model. Provide your work in detail. Include source of data among 2-3 references. Ensure that the objective of the study is included in your write up before presenting the regression model

## Data

 High School GPA SAT Verbal SAT Math Paralegal GPA 3.25 480 410 3.21 1.80 290 270 1.68 2.89 420 410 3.58 3.81 500 600 3.92 3.13 500 490 3.00 2.81 430 460 2.82 2.20 320 490 1.65 2.14 530 480 2.30 2.63 469 440 2.33 the objective of this study is to see the influence of high school GPA and SAT math on paralegal GPA. High School GPA SAT Math Paralegal GPA 3.25 410 3.21 1.80 270 1.68 2.89 410 3.58 3.81 600 3.92 3.13 490 3.00 2.81 460 2.82 2.20 490 1.65 2.14 480 2.30 2.63 440 2.33

SAT Math 3.25 1.8 2.89 3.81 3.13 2.81 2.2000000000000002 2.14 2.63 410 270 410 600 490 460 490 480 440

## Regression

 SUMMARY OUTPUT Regression Statistics Multiple R 0.9192513522 R Square 0.8450230486 Adjusted R Square 0.7933640648 Standard Error 0.361631046 Observations 9 ANOVA df SS MS F Significance F Regression 2 4.2784268082 2.1392134041 16.3577172144 0.003722214 Residual 6 0.7846620807 0.1307770134 Total 8 5.0630888889 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.1695004314 0.688875302 -0.2460538662 0.8138416692 -1.855117572 1.5161167091 -1.855117572 1.5161167091 X Variable 1 1.284124913 0.2647696789 4.8499696726 0.0028517397 0.6362568478 1.9319929782 0.6362568478 1.9319929782 X Variable 2 -0.0013953127 0.0018757414 -0.7438726412 0.485053775 -0.0059850866 0.0031944612 -0.0059850866 0.0031944612 RESIDUAL OUTPUT Observation Predicted Y Residuals 1 3.4318273251 -0.2218273251 the results of regression show that the coefficient of high school GPA is significant with p-value 0.002852 2 1.7651899805 -0.0851899805 the coefficient of SAT math score is insignificant with pvalue 0.485 3 2.9695423564 0.6104576436 alpha in this test is 0.05. 4 3.8858278617 0.0341721383 the coefficient of determination in this regression is 0.845 which means that 84% of variation paralegal GPA is explained by high school GPA, fairly high determination. 5 3.1661073188 -0.1661073188 6 2.7970467279 0.0229532721 7 1.9718711497 -0.3218711497 8 1.908776782 0.391223218 9 2.5938104978 -0.2638104978

X Variable 1 Line Fit Plot

Y 3.25 1.8 2.89 3.81 3.13 2.81 2.2000000000000002 2.14 2.63 3.21 1.68 3.58 3.92 3 2.82 1.65 2.2999999999999998 2.33 Predicted Y 3.25 1.8 2.89 3.81 3.13 2.81 2.2000000000000002 2.14 2.63 3.4318273250949476 1.7651899805203763 2.9695423564190655 3.8858278616601112 3.1661073188169802 2.7970467279303928 1.9718711497376176 1.9087767820482211 2.593810497772286X Variable 1

Y

X Variable 2 Line Fit Plot

Y 410 270 410 600 490 460 490 480 440 3.21 1.68 3.58 3.92 3 2.82 1.65 2.2999999999999998 2.33 Predicted Y 410 270 410 600 490 460 490 480 440 3.4318273250949476 1.7651899805203763 2.9695423564190655 3.8858278616601112 3.1661073188169802 2.7970467279303928 1.9718711497376176 1.9087767820482211 2.593810497772286X Variable 2

Y

X Variable 1 Line Fit Plot

Y 3.25 1.8 2.89 3.81 3.13 2.81 2.2000000000000002 2.14 2.63 3.21 1.68 3.58 3.92 3 2.82 1.65 2.2999999999999998 2.33 Predicted Y 3.25 1.8 2.89 3.81 3.13 2.81 2.2000000000000002 2.14 2.63 3.4318273250949476 1.7651899805203763 2.9695423564190655 3.8858278616601112 3.1661073188169802 2.7970467279303928 1.9718711497376176 1.9087767820482211 2.593810497772286X Variable 1

Y

X Variable 2 Line Fit Plot

Y 410 270 410 600 490 460 490 480 440 3.21 1.68 3.58 3.92 3 2.82 1.65 2.2999999999999998 2.33 Predicted Y 410 270 410 600 490 460 490 480 440 3.4318273250949476 1.7651899805203763 2.9695423564190655 3.8858278616601112 3.1661073188169802 2.7970467279303928 1.9718711497376176 1.9087767820482211 2.593810497772286X Variable 2

Y