Question

Based on the graph depicting the relationship between two variables, you would conclude the 10 variable 2 variable 1 A independent variable: discrete/nominal; relationship best tested with univariate test (e.g. analysis of variance) B. independent variable: continuous; relationship best tested with bivariate test (e.g. linear regression) O dependent variable: discrete/nominal relationship best tested with contingency test (eg, chi-square) D. dependent variable: continuous; relationship best tested with bivariate test (e.g. linear regression)

Answer 1

In the given graph, variable 2 is plotted as a function of variable 1. Hence variable 1 is the independent variable. This variable is taking only three allowed values. Hence it is a discrete variable, also called the nominal variable. The other variable used is variable 2. The value of this variable is dependent on the variable 1, hence it is a dependent variable. The values assumed by this variable lie in the range 0-10 and it also assumes intermediate values. Hence it is a continuous variable.

Thus to summarize we have:

1. The dependent variable is continuous

2. Independent variable is discrete/nominal

Linear regression is a model that can be employed when both the dependent and the independent variables are continuous. In linear regression, the variation in the dependent variable is determined as a function of the independent variable. The underlying assumption is a linear variation. The model fits the data to predict the slope and the y-intercept.

Chi-square test is performed when we have two groups and the data pattern in each group is discretized into finite bins. Since the data can be represented as a contingency table, this is also called as the contingency test.

Analysis of Variance (ANOVA) is a test performed when comparing two or more data groups. The data in each of the groups can be continuous.

Univariate refers to a dataset that has just one variable, while bivariate refers to the dataset that has two variables. Here we have a dataset that has two variables. Hence it is clearly a bivariate dataset and hence requires a test that can analyze bivariate data.

Thus, the best data that can be used for our data would be an ANOVA test with bivariate variance.

Hence the correct option is option A.