Pedigree vs. Grit Case Solution
Question: 1 (b) The situation where R-squared will be higher irrespective of its usefulness is where more than the required number of repressors has been put in the model as well as amount of co-linearity between the repressors is of high value of R-squared.
Question: 1 (c)
MANAGER | RET | GRI | SAT | MBA | AGE | TEN |
beta | -0.1214 | 0.0937 | -0.0103 | -0.0801 | -0.0691 | |
BOB | 103.0652 | 1 | 1042 | 0 | 35 | 5 |
ROCKEFELLER | 132.383 | 1 | 1355 | 1 | 32 | 2 |
The above chart shows the RET calculated for Bob & Rockefeller, as well as the factor important to validate the regression isits linearity. If the number of regressors is more than required, then linearity will be affected which would result in an increase of the linearity.
Question: 2 (a)
MANAGER | RET | GRI | SAT | MBA | AGE | TEN |
BOB | -1.7 | 1 | 1042 | 0 | 35 | 5 |
ROCKEFELLER | 0.4 | 1 | 1355 | 1 | 32 | 2 |
The illustration above shows the linear regression analysis of RET of Bob and Rockefeller.As the SAT, AGE, GRI& AGE are the factors which hold a significance level of 5% apart from the MBA & TEN, which are non-crucial factor. These factors are important in determining who will perform best, hence depending on the composite values of the SAT, GRI, AGE, TEN and MBA of both the candidates, evaluating the RET, Putney is expected to outperform Bob.
Question: 2 (b) Since Putney holds an MBA degree, he is expected to obtain higher return as compared to Bob who does not hold MBA degree based on the calculation done in previous charts.
Question: 3 (a) At5% significance level,Bob,if he attended Princeton instead of Ohio State, then yesthe returns would be higher as the coefficient of SAT is positive and the coefficient of p value is also positive.
Question: 3 (b) Yes, the question asks to validate that at 10% confidence level, as the coefficient of GRI is less than -1. If he were to manage a growth fund instead of an income fund, then he would achieve at least 1% higher return.
Question: 4 (a)
Regression Statistics | |
Multiple R | 0.019136 |
R Square | 0.000366 |
Adjusted R Square | -0.00149 |
Standard Error | 8.508476 |
Observations | 540 |
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -0.72376 | 0.594258 | -1.21792 | 0.223787 | -1.89111 | 0.443589 | -1.89111 | 0.443589 |
MBA (X) | 0.334942 | 0.754483 | 0.443936 | 0.657267 | -1.14715 | 1.817035 | -1.14715 | 1.817035 |
The above equation shows the linear regression equation calculated by taking MBA as independent variable (x) , while keeping all other TEN, AGE,GRI & SAT factors constant. Although there is no substantial evidence in regression table-1 that the person with MBA value=1 outperforms the one with MBA value=0, the coefficient for MBA is negative and its probability of affecting favorably is very high. Hence, from Table-1, the management is not sure whether it would make a difference.
Question: 4 (b) The Beta and the coefficient of MBA are inversely related. If the Beta is used as independent variable (x), it should increase the value of the coefficient of MBA, whichis currently at negative 2.64216 to even positive………………..
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