Applications of Inference



Applications of Inference

Introduction

A study has recently been published in “Unknown Sport Magazine” that proposes what has been suspected by many baseball fans already. Research entails that “Baseball players who weight over 200 lb hit more home run than those under 200 lb. Researchers discover that food supplement medication were use by 10 % of the player to gain weight. Baseball player salary is higher for those who weight at least 200 lb”. To test the hypothesis presented in the study, data regarding baseball players is gathered and then bivariate analysis is used to see whether those data show any evidence of a causal relationship between X and Y i.e. weight and home run. Different forms of bivariate analysis i.e. scatter plot, correlation and regression will be performed for a better analysis of the relationship between two variables.



Discussion

Bivariate analysis

Bivariate analysis is a statistical analysis of a pair of variables. Such analysis can take the form of; for example, scatter plot, cross-tabulation, correlation, one-way ANOVA, or simple regression. It is a step often taken after a Univariate analysis of the data but prior to a multivariate analysis. Hypotheses of “association” and causality are tested with bivariate analysis. Association, in its simplest form, simply denotes the extent to which it becomes easier for predicting a value for the Dependent variable if a case's value is known on the independent variable. A measure of association is beneficial for understanding this relationship. These measures of association relate to how much better this prediction becomes with knowledge of the IV or how well an independent variable relates to the dependent variable.

Scatter Plot

Correlation between two variables may be visualized via scatter-plots—that is, by arranging the values of one variable on one axis and the corresponding values of another variable on another axis. In scatter plots, points falling close to a straight line imply strong correlation, whereas a cloud of points are more suggestive of a weak correlation or a lack of one. Similarly, if most points are in the bottom-left and top-right quadrants, a positive relationship is plausible, whereas if most points are in the top left and bottom right, a negative relationship is likely. In our case, scatter plot depicts a positive relationship between two variables.

Bivariate Regression Analysis

There are several ways in which a regression analysis can be carried out. A graphical approach (as shown below) simply plot Y against X and superimpose a curve that traces out the conditional Y means across the range of X. This strategy is often useful for exploring bivariate data; however, the sample estimates of the conditional Y means are likely to be somewhat unreliable and unstable since there are usually only a small number of observations at each distinct value of X.

Graphical Representation of the Regression Line on a Scatter Diagram

Since the scatterplot shows points that are close to a straight line reasonably, therefore, it implies a high correlation for our results.

Linear Regression Equation

The simplest function for relating the variables is linear in ...