State whether each of the following statements is true, false or uncertain. Expl

Question

State whether each of the following statements is true, false or uncertain. Explain fully why. (a) If a null hypothesis is not rejected, then it is true. (b) A higher R^2 value in a simple linear regression implies that the independent variable explains less portion of the variation of the dependent variable. (c) If there is an intercept in the linear regression model, the estimated element of_i(= element of_i) will always sum up to zero. (d) Gauss-Markov theorem implies that you can get the best unbiased estimator by OLS estimation under the normal assumption. (e) The best unbiased estimator always has a smaller MSE than other estimators.

Explanation / Answer

a) the null hypothesis is not rejected means it is not ture because some times the null hypothesis may be false. in some situations if we accept the null hypothesis in some situations it may be rejected. thats y not rejected mean it may be true or it may be falls.

b) the given statment is true because R-sqaure intrepet the percentage of the response variable variation that is expalined by a linear model.

c) the given statement is true when the intercept is include in the regression the sum is also zero

d) the statment is false because the errors need not be normal.

e) the statement is true because by carmer rao inequality the best unbiased estimator always have the mse than others.

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