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Correlation Coefficient Interpretation Quiz

Created by
@InvincibleMarimba

What determines the coordinates of the axes in a scatterplot?

• The average of the data values
• The number of data points
• The smallest and largest data values of the variables (correct)
• The type of relationship between the variables
• In a scatter diagram, what is the variable called that is represented on the x-axis?

• Explanatory variable
• Independent variable (correct)
• Control variable
• Dependent variable
• When plotting a scatter diagram, what does not joining the points signify?

• No data available
• Relationship between variables not assumed (correct)
• Data is too scattered
• Points are not related
• What can the pattern of data in a scatterplot indicate about the relationship between two variables?

<p>Type and strength of association</p> Signup and view all the answers

What does the correlation coefficient measure?

<p>Strength and direction of a linear relationship</p> Signup and view all the answers

In correlation analysis, what does a positive correlation between two variables indicate?

<p>Direct relationship</p> Signup and view all the answers

If two variables have a negative correlation, what can be said about their relationship?

<p>They have an indirect relationship</p> Signup and view all the answers

How does correlation coefficient help in decision making?

<p>By measuring association between variables</p> Signup and view all the answers

Study Notes

Correlation Coefficient Formula

• The formula for the correlation coefficient (r) is: r = Σ((xi - x̄)(yi - ȳ)) / sqrt(Σ(xi - x̄)² * Σ(yi - ȳ)²)
• Where: r = correlation coefficient, n = number of data pairs, xi = observed data for the independent variable, yi = observed data for the dependent variable, x̄ = mean of xi, ȳ = mean of yi

Strength of Relationship

• The strength of the relationship between two variables is determined by the correlation coefficient (r) value
• 0.00 – 0.19: very weak relationship
• 0.20 – 0.39: weak relationship
• 0.40 – 0.59: moderate relationship
• 0.60 – 0.79: strong relationship
• 0.80 – 0.99: very strong relationship
• 1: perfect relationship

Hypothesis Testing

• The null hypothesis (H0) states that there is no correlation between the x and y variables in the population (ρ = 0)
• The alternative hypothesis states that there is a correlation between the x and y variables in the population (ρ ≠ 0)

Regression Analysis

• Regression analysis is a technique used to predict the value of one variable (Y) based on the value of another variable (X)
• It helps to create a straight line that best fits the data, known as the line of best fit
• The regression line minimizes the sum of the squares of the residuals

Scatterplots

• A scatterplot is a graphical representation of the relationship between two quantitative variables
• It has a rectangular coordinate system, with one variable (X) on the x-axis and the other variable (Y) on the y-axis
• Each point on the scatterplot represents a single data point
• Scatterplots can indicate the type of relationship between two variables: positive, negative, or no relationship

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Description

Test your understanding of how to interpret the strength of a relationship between two variables based on the correlation coefficient value. Learn to classify relationships as very weak, weak, moderate, strong, or very strong according to Evans (1996) guidelines.

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