State whether the following statements are true or false and give a brief explanation

If the value of the linear correlation coefficient is zero, then these two variables are independent.

The least square regression line minimizes the sum of errors.

The covariance between any two variables decides the strength of their relation.

The regression coefficient decides the trend and the strength of the relation between the dependent and the independent variables.

(Q2) Define the following terms briefly. (2 marks)

The determinant coefficient.

The deterministic model and the probabilistic model.

(Q3) Answer the following questions briefly. (4 marks)

Explain the meaning of independent and dependent variables for a regression model. Explain the difference between a simple and a multiple regression model.

Compare between the roles of both the regression coefficient and the correlation coefficient. Can the values of regression coefficient and the correlation coefficient have different signs? Explain.

The similarities and the difference between the normal, the standard normal.

Can the values of the regression coefficient and the correlation coefficient have different signs? Explain.

If the correlation coefficient between two variables equals zero, then the two variables are independent. Comment.

Why is the random error included in a regression model?