State whether the following statements are true or false and also give the reason in support of your answer.

(i) We define three indicator variables for an explanatory variable with three categories.

(ii) If the coefficient of determination is 0.833, the number of observations and explanatory variables are 12 and 3, respectively, then the Adjusted R² will be 0.84.

(iii) For a simple regression model fitted on 15 observations, if we have h₁ = 0.37, then it is an indication to trace the leverage point in the regression model.

(iv) In a regression model  is not rejected, then the variable X₁ will remain in the model.

(v) The logit link function is log [-log(1-π)].

(i) False
Reason: For an explanatory variable with three categories, we define two indicator (dummy) variables, not three. The number of indicator variables is always one less than the number of categories to avoid multicollinearity (the dummy variable trap).

(ii) False
Reason: Adjusted R² is always less than or equal to R² unless the added variables significantly improve the model. Given R² = 0.833, ____ ________ __________ _______ ____ ___ ________.
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