Q4. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

 

The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the regression equation is modeling the data.

Step-by-Step Solution

Answer

The given statement is True.

Step 1. State the concept.

• A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another. 
• In positively correlated variables, the value increases or decreases in tandem. 
• In negatively correlated variables, the value of one increases as the value of the other decreases.
• Correlation coefficients are expressed as values between $+1$ and $-1$.
• A coefficient of $+1$ indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable.
• A coefficient of $-1$ indicates a perfect negative correlation: A change in the value of one variable predicts a change in the opposite direction in the second variable. 
• Lesser degrees of correlation are expressed as non-zero decimals. A coefficient of zero indicates there is no discernible relationship between fluctuations of the variables. 

Step 2. Explanation of the statement.

The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the regression equation is modeling the data.

So, the given statement is True.

Step 3. Write whether the statement is true or false.

Therefore, the given statement, “The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the regression equation is modeling the data.” is true.