Question

A statistical technique that helps identify commonalities between different sets of data is called:

a) Regression

b) Standard Deviation

c) Correlation

d) Factor Analysis

Answer 1

The correct answer is option c) Correlation. Correlation is a statistical technique that measures the strength and direction of the relationship between two variables.

Step-by-step explanation:

Correlation is a statistical technique that measures the strength and direction of the relationship between two variables. It helps identify commonalities between different sets of data by determining how closely they are related. For example, if there is a high positive correlation between the number of hours studied and exam grades, it indicates that studying more hours is associated with higher grades.

In practical terms, correlation can be represented by a scatter plot, which is a graph that displays the relationship between two variables. Each data point on the plot represents a pair of values for the variables being studied. If the plot forms a clear pattern or trend, it suggests a linear relationship between the variables. The correlation coefficient, calculated using regression analysis, quantifies the strength and direction of this linear relationship. It ranges from -1 to 1, with values close to 1 indicating a strong positive correlation, values close to -1 indicating a strong negative correlation, and values close to 0 indicating no correlation.

To summarize, correlation is a statistical technique that helps identify commonalities between different sets of data by measuring the strength and direction of the relationship between two variables. It is represented by a scatter plot and quantified by the correlation coefficient.

Answer 2

A statistical technique that helps identify commonalities between different sets of data is called c) Correlation. option C is correct.

Step-by-step explanation:

Correlation is a statistical technique that helps identify commonalities between different sets of data. It measures the strength and direction of a linear relationship between two variables. The correlation coefficient, denoted by "r," ranges from -1 to 1. A positive correlation indicates a direct relationship, while a negative correlation suggests an inverse relationship. The closer the correlation coefficient is to 1 or -1, the stronger the relationship between the variables.

In the context of the options provided, regression (a) is a technique used to predict one variable based on the value of another, standard deviation (b) measures the spread of data points, and factor analysis (d) is a method to identify underlying factors influencing observed variables. Correlation, however, specifically assesses the association between two variables. Mathematically, the correlation coefficient (r) is calculated as the covariance of the two variables divided by the product of their standard deviations. The formula is expressed as:

`\[ r = \frac{\sum{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sqrt{\sum{(X_i - \bar{X})^2} \sum{(Y_i - \bar{Y})^2}}} \]`

Here,
`\(X_i\)`and
`\(Y_i\)` represent individual data points,
`\(\bar{X}\)` and
`\(\bar{Y}\)` are the means of X and Y, and the numerator and denominator correspond to the covariance and standard deviations, respectively. By computing the correlation coefficient, analysts can discern the strength and direction of the relationship between the two variables, aiding in understanding commonalities in the datasets under consideration.