Question

6) The valid range of sample correlation coefficient is

A) 0 ≤ ? ≤ 1

B) −1 ≤ ? ≤ 1

C) 0 < ? < 1

D) −1 ≤ ? ≤ 1

7) The method used to find the estimate of the parameters in the classic regression model is

called

A) Classic Least Squares

B) Ordinary Least Squares

C) Generalized Least Squares

D) Weighted Least Squares

8) Which of the following statement is true?

A) RSS = TSS + ESS

B) TSS = ESS + RSS

C) ESS = TSS + RSS

D) None of the above

Answer 1

6) −1 ≤ ? ≤ 1

correlation coefficient measures both the strength and direction of the linear relationship between two continuous variables. Values can range from -1 to +1.

-The extreme values of -1 and 1 indicate a perfectly linear relationship where a change in one variable is accompanied by a perfectly consistent change in the other

-A coefficient of zero represents no linear relationship.

-the value is in-between 0 and +1/-1, there is a relationship, but the points don’t all fall on a line. As r approaches -1 or 1, the strength of the relationship increases and the data points tend to fall closer to a line.

7)  Ordinary Least Square

The concepts of population and sample regression functions are introduced, along with the ‘classical assumptions’ of regression. These assumptions allow the ordinary least squares (OLS) estimators

8) TSS = ESS + RSS

Explained sum of squares (ESS):

Also known as the explained variation, the ESS is the portion of total variation that measures how well the regression equation explains the relationship between X and Y.

You compute the ESS with the formula

Residual sum of squares (RSS): This expression is also known as unexplained variation and is the portion of total variation that measures discrepancies (errors) between the actual values of Y and those estimated by the regression equation.

You compute the RSS with the formula

Total sum of squares (TSS):

The sum of RSS and ESS equals TSS.