Question

1. Describetherelationshipbetweentwovariableswhenthe correlation coefficient r is a) near –1 b) near 0 c) near +1

2. What is the meaning of the “least-squares” criterion?

3. “Correlation does not imply causation.” Explain.

Answer 1

Q1) When r = -1, the two variables are perfectly negatively correlated.

When r = +1, the two variables are perfectly positively correlated.

  When r = 0, the two variables are not correlated.

Q2) Least squares criteria refers to the formula used as a measure or estimate the regression line that best fits the data. The line is so fitted that the residual sum of squares is least.e.g If   is the actual observations and is the estimated observation.

Least Square Criteria is based on

  

where is the residual or error.

Also   , the problem is to estimate a,b so that is minimum.

Q3) Correlation is a mutual relationship or a connection between two variables. Causation is the relationship between cause and effect. So, when a cause results in an effect, that's a causation. In other words, correlation between two events or variables simply indicates that a relationship exists, whereas causation is more specific and says that one event actually causes the other. When we say that correlation does not imply cause, we mean that just because you can see a connection or a mutual relationship between two variables, it doesn't necessarily mean that one causes the other.