Question

Decide (with short explanations) whether the following statements are true or false.

) Them ae t pdicen st ame t eulbeant Than global F-test is highly significant. For this reason, it is better not to remove both predictors simultaneously depend variable, or both, does not change the regression R2 the same or fall must fail to reject it at a significance level of a-0.10. o) The process of multiplying the dependent variable by a constant, adding a constant to the p) If an extra explanatory variable is added to a regression, the estimator of σ (%) will remain q) If we fail to reject the null hypothesis (Ho) at a significance level of α-0.05, then we also

Answer 1

Solution

Part (n)

Since global F-test is highly significant and two predictors are not significant, the response variable is adequately explained by the other variables.

So, retaining the insignificant predictors is NOT advisable. Answer 1

Part (o)

R² = Cov²/{Var(X) x Var(Y)}, where X = independent variable and Y is dependent variable.

Adding a constant does not alter covariance or variance. However, multiplication by a constant, say c, would imply the covariance gets multiplied by c which in turn means Cov² gets multiplied by c². Var(Y) also gets multiplied by c². These two c², one in numerator and the other in the denominator get cancelled. Thus,

R² remains unchanged. Answer 2

Part (p)

When an extra explanatory variable is added to a regression, the regression sum of squares would increase, however small (the exact quantum would depend on how significant that variable is). Resultantly, error sum of squares would come down which implies estimator of σ would fall. Answer 3

Part (q)

Critical value for all test statistics at α = 0.05 would be farther away from that at α = 0.10......................... (1)

We fail to reject the null hypothesis if critical value is beyond the observed value of the test statistic. ...... (2)

(1) and (2) =>

failing to reject null hypothesis at α = 0.10 also means failing to reject null hypothesis at α = 0.05 and not necessarily vice-versa.

So, the given statement is NOT universally true. Answer 4

DONE

[Going beyond,

To elaborate on reasoning of Part (q),

Critical value at α = 0.05 would be greater than that at α = 0.10 for all two-sided and > type one-sided tests; but less than for < type one-sided tests.

For all two-sided and > type one-sided tests, acceptance region is: observed value < critical value and for for < type one-sided tests, it is observed value > critical value]

Complete