Performance Management - What are the drivers of success?

Regression Analysis Project

Professor Sangit Chatterjee

Rudy Parker

[email protected]

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Simple Regression analysis MBA GPA Versus GMAT

Regression Analysis: MBA GPA versus GMAT

The regression equation isMBA GPA = 1.39 + 0.00311 GMAT

Predictor Coef SE Coef T PConstant 1.3923 0.1387 10.04 0.000GMAT 0.0031142 0.0002403 12.96 0.000

S = 0.236514 R-Sq = 45.6% R-Sq(adj) = 45.4%

PRESS = 11.4007 R-Sq(pred) = 44.60%

Analysis of Variance

Source DF SS MS F PRegression 1 9.3921 9.3921 167.90 0.000Residual Error 200 11.1877 0.0559 Total 201 20.5798

5 rows with no replicates

Unusual Observations

Obs GMAT MBA GPA Fit SE Fit Residual St Resid 3 510 3.7450 2.9805 0.0225 0.7645 3.25R 21 540 3.5460 3.0739 0.0184 0.4721 2.00R 39 680 2.9430 3.5099 0.0306 -0.5669 -2.42R 49 570 2.6080 3.1674 0.0167 -0.5594 -2.37R 63 750 3.8180 3.7279 0.0457 0.0901 0.39 X

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74 500 3.5680 2.9494 0.0242 0.6186 2.63R 95 520 3.5170 3.0117 0.0210 0.5053 2.15R106 740 3.5200 3.6968 0.0435 -0.1768 -0.76 X107 570 2.5090 3.1674 0.0167 -0.6584 -2.79R127 670 3.9520 3.4788 0.0286 0.4732 2.02R132 400 2.4680 2.6380 0.0448 -0.1700 -0.73 X137 760 3.8800 3.7591 0.0479 0.1209 0.52 X142 460 3.4660 2.8248 0.0318 0.6412 2.74R149 590 2.7080 3.2297 0.0171 -0.5217 -2.21R155 760 4.0000 3.7591 0.0479 0.2409 1.04 X173 630 3.8940 3.3542 0.0216 0.5398 2.29R176 560 3.6230 3.1362 0.0169 0.4868 2.06R196 500 3.6400 2.9494 0.0242 0.6906 2.94R

R denotes an observation with a large standardized residual.X denotes an observation whose X value gives it large influence.

Durbin-Watson statistic = 1.92488

No evidence of lack of fit (P >= 0.1).

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This simple regression analysis is looking at the response of MBA GPA scores to the explanatory variable GMAT. The R-Squared statistic is 45.6%, which means that 45.6% of the MBA GPA score is determined by the GMAT score. This is a reasonably strong positive correlation. It is a reflection of the fact that SSR is 9.39 over SST of 20.79. This means the error is only 11.18.

There were 202 observations made. The GMAT scores of the MBA students varied from 400 to 760. The GPA scores varied from 2.4 to 4. The line in the figure is the least-squares regression line for predicting GPA from GMAT. The equation of the line is

Predicted GPA = 1.39 + 0.00311 x GMAT

GPA rises by 0.00311 for every point rise in GMAT score.

Testing the confidence interval of 95% for the slope b of the regression line is

b +/- t* Seb

t* is the value for the t(n-2) density curve.

B = 0.0031142 +/- 1.97 * 0.0002403 (0.002640809, 0.003587591)

Testing the null hypothesis

H: B = 0 H: B does not equal 0

P= 0Alpha = 0.05

Therefore P < alpha & we reject the null hypothesis.

My conclusion is that GPA can be predicted from GMAT Scores.

Residual Plots for MBAGPA

One-way ANOVA: MBAGPA versus GMAT

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Source DF SS MS F PGMAT 31 11.2455 0.3628 6.61 0.000Error 170 9.3343 0.0549Total 201 20.5798

S = 0.2343 R-Sq = 54.64% R-Sq(adj) = 46.37%

Individual 95% CIs for Mean Based on Pooled StDev

Level N Mean StDev -------+---------+---------+---------+--400 1 2.4680 * (-------*-------)430 3 2.6843 0.1635 (----*---)450 1 2.7360 * (-------*------)460 6 2.8713 0.3118 (--*--)470 6 2.8057 0.1378 (--*--)480 5 3.0168 0.1978 (--*---)490 4 2.8965 0.2281 (---*---)500 7 3.0649 0.4108 (--*--)510 9 3.0948 0.3097 (--*-)520 11 3.0297 0.2477 (-*--)530 4 3.0195 0.1642 (---*---)540 15 3.0973 0.2043 (-*-)550 6 3.3063 0.1712 (--*--)560 12 3.0872 0.2708 (-*--)570 21 3.0350 0.2312 (-*)580 11 3.2226 0.1961 (--*-)590 9 3.0913 0.2472 (--*-)600 12 3.2447 0.1590 (-*-)610 13 3.2093 0.2230 (-*--)620 3 3.4277 0.1328 (---*----)630 4 3.4870 0.3126 (---*---)640 5 3.2792 0.1564 (---*--)650 5 3.4414 0.1801 (--*---)660 3 3.4580 0.1963 (----*---)670 10 3.5587 0.2121 (-*--)680 4 3.3727 0.3693 (---*---)690 4 3.5960 0.1742 (---*---)700 3 3.7873 0.0783 (---*----)720 1 3.7200 * (-------*-------)740 1 3.5200 * (-------*------)750 1 3.8180 * (-------*------)760 2 3.9400 0.0849 (-----*----) -------+---------+---------+---------+-- 2.40 3.00 3.60 4.20

Pooled StDev = 0.2343

It’s interesting to note that the confidence intervals for GMAT scores to MBA GPA seem to be the largest at either ends of the GMAT spectrum. This seems to suggest that people with very high or very low scores need to be looked at slightly differently from the usual. Perhaps certain people are very bad at standardized tests and get nervous. In an MBA program they could perform far higher than anticipated. Equally, there are some individuals who are very good at quantitative analysis and tests, yet they cannot work in

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teams due to other factors such as lack of team-working abilities or low ‘EQ’. This would thus bring their GPA down considerably below that anticipated.

Multiple Regression Analysis MBA GPA versus GMAT, UGPA, Age

Regression Analysis: MBA GPA versus GMAT, UGPA, Age

The regression equation isMBA GPA = 0.871 + 0.00228 GMAT + 0.297 UGPA + 0.00543 Age

Predictor Coef SE Coef T PConstant 0.8713 0.2634 3.31 0.001GMAT 0.0022825 0.0002649 8.62 0.000UGPA 0.29731 0.04300 6.91 0.000Age 0.005435 0.008088 0.67 0.502

S = 0.212057 R-Sq = 56.7% R-Sq(adj) = 56.1%


Source DF SS MS F PRegression 3 11.6761 3.8920 86.55 0.000Residual Error 198 8.9037 0.0450Total 201 20.5798

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Source DF Seq SSGMAT 1 9.3921UGPA 1 2.2637Age 1 0.0203


Obs GMAT MBA GPA Fit SE Fit Residual St Resid 3 510 3.7450 3.2794 0.0470 0.4656 2.25R 20 690 3.8420 3.3344 0.0412 0.5076 2.44R 34 430 2.8120 2.7542 0.0649 0.0578 0.29 X 39 680 2.9430 3.4696 0.0295 -0.5266 -2.51R 48 650 3.6350 3.1927 0.0408 0.4423 2.13R 70 460 2.7150 2.8183 0.0723 -0.1033 -0.52 X 74 500 3.5680 2.9137 0.0659 0.6543 3.25RX 87 670 3.7930 3.2662 0.0399 0.5268 2.53R107 570 2.5090 3.0064 0.0272 -0.4974 -2.37R132 400 2.4680 2.9573 0.0655 -0.4893 -2.43RX140 460 2.7040 3.0374 0.0522 -0.3334 -1.62 X142 460 3.4660 2.7994 0.0296 0.6666 3.17R154 670 3.6260 3.6825 0.0692 -0.0565 -0.28 X170 610 2.8570 3.3139 0.0183 -0.4569 -2.16R173 630 3.8940 3.1198 0.0384 0.7742 3.71R176 560 3.6230 3.4618 0.0524 0.1612 0.78 X196 500 3.6400 3.2205 0.0462 0.4195 2.03R


Regression Analysis: MBA GPA versus GMAT, UGPA, Age

The regression equation isMBA GPA = 0.871 + 0.00228 GMAT + 0.297 UGPA + 0.00543 Age

Predictor Coef SE Coef T PConstant 0.8713 0.2634 3.31 0.001GMAT 0.0022825 0.0002649 8.62 0.000UGPA 0.29731 0.04300 6.91 0.000Age 0.005435 0.008088 0.67 0.502

S = 0.212057 R-Sq = 56.7% R-Sq(adj) = 56.1%

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Source DF Seq SSGMAT 1 9.3921UGPA 1 2.2637Age 1 0.0203


Obs GMAT MBA GPA Fit SE Fit Residual St Resid 3 510 3.7450 3.2794 0.0470 0.4656 2.25R 20 690 3.8420 3.3344 0.0412 0.5076 2.44R 34 430 2.8120 2.7542 0.0649 0.0578 0.29 X 39 680 2.9430 3.4696 0.0295 -0.5266 -2.51R 48 650 3.6350 3.1927 0.0408 0.4423 2.13R 70 460 2.7150 2.8183 0.0723 -0.1033 -0.52 X 74 500 3.5680 2.9137 0.0659 0.6543 3.25RX 87 670 3.7930 3.2662 0.0399 0.5268 2.53R107 570 2.5090 3.0064 0.0272 -0.4974 -2.37R132 400 2.4680 2.9573 0.0655 -0.4893 -2.43RX140 460 2.7040 3.0374 0.0522 -0.3334 -1.62 X142 460 3.4660 2.7994 0.0296 0.6666 3.17R154 670 3.6260 3.6825 0.0692 -0.0565 -0.28 X170 610 2.8570 3.3139 0.0183 -0.4569 -2.16R173 630 3.8940 3.1198 0.0384 0.7742 3.71R176 560 3.6230 3.4618 0.0524 0.1612 0.78 X196 500 3.6400 3.2205 0.0462 0.4195 2.03R


Residual Plots for MBA GPA

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The R-Squared for this model was 56.7, which means that there is quite a good positive correlation between MBA GPA and GMAT, Undergraduate GPA and Age.

The Hypothesis test

Alpha is 0.05%

H: O, B1 = B2 = B3 = 0

H1: At least one of these is non-Zero

1) B1 P < alpha ( P = 0, alpha = 0.05) Therefore reject null hypothesis. Gmat is a good predictor of MBA GPA

2) B2 P< alpha (P = 0, alpha = 0.05). Therefore reject null hypothesis. Undergraduate GPA is a good predictor of MBA GPA

3) B3 P> alpha (P = 0.502, alpha=0.05). Therefore accept null hypothesis. Age is not a good indicator of MBA GPA.

The F statistic is very high. MSE is much less than MSR. Therefore this is a good model. The one caveat is that Age is not a good indicator. This could be rejected from the model to create a better regression analysis according to Ockham’s principle; you should have as few variables as possible to predict the relationship between variables and MBA GPA.

My conclusion is that MBA GPA can be predicted to a large extent through Undergraduate GPA and GMAT scores.

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Regression Analysis: MBA GPA versus UGPA

Weighted analysis using weights in MBA GPA

The regression equation isMBA GPA = 1.78 + 0.485 UGPA

Predictor Coef SE Coef T PConstant 1.7815 0.1277 13.96 0.000UGPA 0.48509 0.04297 11.29 0.000

S = 0.449942 R-Sq = 38.9% R-Sq(adj) = 38.6%

PRESS = 40.7521 R-Sq(pred) = 38.53%




Obs UGPA MBA GPA Fit SE Fit Residual St Resid 12 3.96 3.8360 3.7049 0.0474 0.1311 0.58 X 20 2.59 3.8420 3.0355 0.0235 0.8065 3.53R 25 2.94 3.6970 3.2072 0.0178 0.4898 2.10R 44 3.96 3.6610 3.7044 0.0474 -0.0434 -0.19 X 48 2.38 3.6350 2.9355 0.0300 0.6995 2.99R 57 2.92 2.5850 3.1999 0.0178 -0.6149 -2.20R 74 2.45 3.5680 2.9680 0.0277 0.6000 2.54R 85 2.83 3.6820 3.1538 0.0184 0.5282 2.26R 87 2.49 3.7930 2.9899 0.0263 0.8031 3.50R127 3.76 3.9520 3.6074 0.0395 0.3446 1.55 X132 3.40 2.4680 3.4294 0.0264 -0.9614 -3.37R137 3.77 3.8800 3.6122 0.0399 0.2678 1.19 X140 3.35 2.7040 3.4075 0.0250 -0.7035 -2.58R155 3.91 4.0000 3.6768 0.0451 0.3232 1.47 X173 2.32 3.8940 2.9089 0.0320 0.9851 4.36R176 3.90 3.6230 3.6743 0.0449 -0.0513 -0.22 X

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200 4.00 3.7200 3.7219 0.0488 -0.0019 -0.01 X


* WARNING * the prediction interval output assumes a weight of 1. An Adjustment must be made if a weight other than 1 is used.

Predicted Values for New Observations

Regression Analysis: MBAGPA versus GMAT, UGPA

The regression equation isMBAGPA = 1.02 + 0.00222 GMAT + 0.302 UGPA

Predictor Coef SE Coef T PConstant 1.0234 0.1346 7.60 0.000GMAT 0.0022226 0.0002491 8.92 0.000UGPA 0.30163 0.04245 7.10 0.000

S = 0.211764 R-Sq = 56.6% R-Sq(adj) = 56.2%

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Source DF Seq SSGMAT 1 9.3921UGPA 1 2.2637


Obs GMAT MBAGPA Fit SE Fit Residual St Resid 3 510 3.7450 3.2811 0.0469 0.4639 2.25RX 20 690 3.8420 3.3367 0.0410 0.5053 2.43R 39 680 2.9430 3.4638 0.0282 -0.5208 -2.48R 48 650 3.6350 3.1857 0.0394 0.4493 2.16R 57 500 2.5850 3.0167 0.0236 -0.4317 -2.05R 74 500 3.5680 2.8725 0.0242 0.6955 3.31R 87 670 3.7930 3.2639 0.0397 0.5291 2.54R 95 520 3.5170 3.3097 0.0460 0.2073 1.00 X107 570 2.5090 3.0097 0.0267 -0.5007 -2.38R132 400 2.4680 2.9371 0.0581 -0.4691 -2.30RX137 760 3.8800 3.8510 0.0448 0.0290 0.14 X142 460 3.4660 2.8044 0.0287 0.6616 3.15R155 760 4.0000 3.8911 0.0468 0.1089 0.53 X170 610 2.8570 3.3179 0.0173 -0.4609 -2.18R173 630 3.8940 3.1247 0.0376 0.7693 3.69R176 560 3.6230 3.4451 0.0460 0.1779 0.86 X196 500 3.6400 3.2278 0.0448 0.4122 1.99 X

Therefore 56.6% of the MBA GPA is determined by GMAT score and undergraduate GPA. However it would be interesting to see how this correlation works with data such as Undergraduate institution. For example, if you could determine a correlation between MBA GPA, GMAT, UG GPA and institution and major, then you could perhaps be in a strong position to determine with around 70% accuracy what the MBA GPA of a potential student is.

Clearly this information is extremely valuable to business schools, since GPA scores is a major factor in determining the employability of its students. This is especially the case with fields such as finance and consultancy, where less than a 3.5 GPA is rarely looked

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at. Therefore I decided to take a look at Undergraduate schools to determine some correlation. I did not want to include race or sex as a defining factor in my report for ethical reasons.

MBA GPA V SCHOOL

Unfortunately there doesn’t seem to be a large correlation between schools and MBA GPA, only around 12%

Regression Analysis: MBA GPA versus School

The regression equation isMBA GPA = 2.78 + 0.113 School

Predictor Coef SE Coef T PConstant 2.78497 0.07521 37.03 0.000School 0.11254 0.02075 5.42 0.000

S = 0.299501 R-Sq = 12.8% R-Sq(adj) = 12.4%

Residual Plots for MBA GPA

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I thought it would be interesting to see if there was a better correlation between undergraduate major and MBA GPA. Generally, students who have studies subjects such as engineering seem to get higher scores. However this may just be anecdotal evidence.

There is only about a 2% correlation for MBA GPA and major, so it appears that this evidence is mainly anecdotal. However I would like to experiment more on this with my own data on methods. For I am relying on the data passed to me. I would ideally like to run some kind of comparison between liberal arts majors/ political science/ Business and finally engineering/ pure science to get a better picture of the correlations.

Regression Analysis: MBA GPA versus Major

The regression equation isMBA GPA = 3.07 + 0.0604 Major

Predictor Coef SE Coef T PConstant 3.06868 0.05129 59.83 0.000Major 0.06040 0.02585 2.34 0.020

S = 0.316490 R-Sq = 2.7% R-Sq(adj) = 2.2%

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Regression Analysis: MBA GPA versus Age

The regression equation isMBA GPA = 3.68 - 0.0212 Age

Predictor Coef SE Coef T PConstant 3.6849 0.2748 13.41 0.000Age -0.02119 0.01142 -1.86 0.065

S = 0.318053 R-Sq = 1.7% R-Sq(adj) = 1.2%

PRESS = 20.7420 R-Sq(pred) = 0.00%



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As you can see from the diagram, the order of correlation of data is in descending order, from MBA to GMAT of 46%, through to MBA to age of 1.7% R-Squared.

Importance of Variables

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GMAT UGPA School Major Age

Variable

Corr

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(%) GMAT

UGPA

SchoolMajor

Age

Conclusion

Therefore I would conclude that the best indication of MBA GPA is undergraduate GPA and GMAT. However people at lowest and highest range of GMAT should probably be looked at more carefully, since other factors seemed to play a much larger part, for these parameters. I would also recommend going into far more detail on schools and undergraduate degree. Perhaps some kind of personality profiling would be useful in order to determine sociability/ extroversion and interpersonal skills that could be factored into the model to achieve an ideal correlation of around 70 % accuracy.

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Correlation between MBA GPA and GMAT/ Undergraduate GPA

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Performance Management - What are the drivers of success?

Business

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