8 Questions
What determines the coordinates of the axes in a scatterplot?
The smallest and largest data values of the variables
In a scatter diagram, what is the variable called that is represented on the x-axis?
Independent variable
When plotting a scatter diagram, what does not joining the points signify?
Relationship between variables not assumed
What can the pattern of data in a scatterplot indicate about the relationship between two variables?
Type and strength of association
What does the correlation coefficient measure?
Strength and direction of a linear relationship
In correlation analysis, what does a positive correlation between two variables indicate?
Direct relationship
If two variables have a negative correlation, what can be said about their relationship?
They have an indirect relationship
How does correlation coefficient help in decision making?
By measuring association between variables
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
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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