The possible range of values for the correlation coefficient is -1.0 to 1.0. In other words, the values cannot exceed 1.0 or be less than -1.0. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

Answer: -0.85 (Option d) is the strongest correlation coefficient which represents the strongest correlation as compared to others.

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

Key similarities Both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.

When you’re looking to build a model, an equation, or predict a key response, use regression. If you’re looking to quickly summarize the direction and strength of a relationship, correlation is your best bet. To further conceptualize your data, make the most out of data visualization software.

There are only three criteria an equation must meet to qualify as a linear relationship:

1. It can have up to two variables.
2. The variables must be to the first power and not in the denominator.
3. It must graph to a straight line.

A nonlinear curve may show a positive or a negative relationship. The slope of a curve showing a nonlinear relationship may be estimated by computing the slope between two points on the curve. The slope at any point on such a curve equals the slope of a line drawn tangent to the curve at that point.

The slope of a line describes a lot about the linear relationship between two variables. If the slope is positive, then there is a positive linear relationship, i.e., as one increases, the other increases. If the slope is 0, then as one increases, the other remains constant.

Common Examples of Positive Correlations. The more time you spend running on a treadmill, the more calories you will burn. Taller people have larger shoe sizes and shorter people have smaller shoe sizes. The longer your hair grows, the more shampoo you will need.

Limitations to Correlation and Regression

• We are only considering LINEAR relationships.
• r and least squares regression are NOT resistant to outliers.
• There may be variables other than x which are not studied, yet do influence the response variable.
• A strong correlation does NOT imply cause and effect relationship.
• Extrapolation is dangerous.