A researcher wished to investigate the effect of the value of a firm (denoted Value) and the capital stock (denoted Captial) on the Investments. Therefore data for 10 companies during 20 years is collected. The researcher is choosing between a pooled OLS, random effect model with company random effects and fixed effect model with company fixed effect. The result is as follows:

 a. Write the fixed effect model using formulas and the variable names from this question.
b. Based on Hausman test, which method is preferred?
c. Based on the description of the data and the Hausman test would you use a fixed or a random effect model?
d. Test the overall significance of the random effect model.

Correlated Random Effects - Hausman Test Equation: Untitled Test cross-section random effects Test Summary Cross-section random Chi-Sa. Statistic Chi-Sa d.f. Prob. 2. 131366 2 0.3445 Cross-section random effects test comoarisons: Variable Fixed Random Var(Diff.) Prob. TAL VALUE 0.310085 0.110124 0.308113 0.000008 0.4332 0.9508 0.109781 0.000031 Dependent Variable: INVESTMENT Method: Panel EGLS (Cross-section random effects) Date: 05/18/21 Time: 14:51 Sample: 1835 1954 Periods included: 20 Cross-sections inciuded: 10 Total panel (balanced) observations: 200 Swamy and Arora estimator of component variances Variable Coefficient Std. Error t-Statistic Prob. TAL 0.308113 0.109781 -57.83441 0.017175 0.010489 28.88930 17.93989 10.46815 -2.001932 0.0000 0.0000 0.0467 VALUE Effects Specification SD. Rho Cross-section random Idiosyncratic random 84.20095 52.70707 0.7180 0.2820 Weighted Statistics Root MSE 52.38817 R-squared 20.25556 Adjusted R-squared 109.3028 S.E. of regression 548004.1 0.682684 Prob(F-statistic) 0.700503 0.767183 Mean dependent var S.D. dependent var Sum squared resid Durbin-Watson stat 52.78556 328.8300 0.000000 F-statistic