Final answer:
To determine how changes in an independent variable affect a dependent variable, one should compute the least-squares regression line and calculate the correlation coefficient. This will quantify the strength and direction of the relationship. For categorical data, a chi-square test of independence can be used to assess the relationship between two factors.
Step-by-step explanation:
To determine the extent to which the conditions of the independent variable determine dependent scores, we should compute the least-squares regression line. This calculation allows us to find the line that minimizes the sum of the squares of the vertical distances of the points from the line.
This line provides us with an equation of the form ý = a + bx, where a is the intercept and b is the slope of the line. The slope, b, represents the change in the dependent variable for a one-unit change in the independent variable.
When examining the relationship between two variables, a commonly used statistic is the correlation coefficient. This coefficient measures the strength and direction of a linear relationship between two variables on a scatter plot. Its value ranges from -1 to 1, where 1 indicates a perfect positive linear association, -1 is a perfect negative linear association, and 0 indicates no linear correlation.
When the correlation coefficient is squared (R-squared), it represents the proportion of variance in the dependent variable that is predictable from the independent variable.
Furthermore, if we are considering categorical data, we can use a test of independence like the chi-square test to assess whether two factors are independent. The null hypothesis of the test is that there is no association between the factors (they are independent), while the alternative hypothesis is that there is an association (they are dependent).