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Questions and Answers
What determines the coordinates of the axes in a scatterplot?
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?
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?
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?
What can the pattern of data in a scatterplot indicate about the relationship between two variables?
What does the correlation coefficient measure?
What does the correlation coefficient measure?
In correlation analysis, what does a positive correlation between two variables indicate?
In correlation analysis, what does a positive correlation between two variables indicate?
If two variables have a negative correlation, what can be said about their relationship?
If two variables have a negative correlation, what can be said about their relationship?
How does correlation coefficient help in decision making?
How does correlation coefficient help in decision making?
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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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