Students' performance in subjects such as mathematics and psychology are compared using correlation and regression analysis in science (Apley & Zhu, 2020). The video explains how to use scatter plots and correlation to visualize a data relationship. It also explains the difference between a scatter plot and a correlation analysis under these headings. A scatter plot depicts the association of two variables, while a correlation analysis is used to assess the degree of the association and determine the direction of the association.

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Variables from the charts
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Scatter diagrams are used to visualize the relationship of two different variables where each can be plotted on the vertical and horizontal axes. In these charts, one variable correlates with one another, respectively.

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What correlation analysis measures
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The analytic is used in measuring the degree of association between two variables. The study analyzes with the strength of the association and the direction of the relationship, and at some point, the significance of the relationship. In this analysis, we are not trying to apply the casual effects or other implications. There are several relationships under this analysis. These may include the linear relationship and the curvilinear relationship.

Linear relationships are types of relationships where one can plot a straight line passing through the plotted variables. In this relation, there are two variables, one on the horizontal axis and the other on the vertical-axis. The variables can align either in a positive or in a negative direction. The curvilinear relationship is a kind of relationship with a curved relation, unlike linear relation in which a straight line can be plotted between points. In curvilinear relation, as x-axis variables increases, the y-variables increase at first and reach a time when it starts reducing or rather decreasing.

Using scatter plots, we can easily determine the strength of the relationship by looking at the closeness or another way by comparing the distance in between the plotted points. When variables are tight to one another, then it means that they have a strong relationship than those away from one another. In addition, we can be able to tell whether there is a relationship between variables or not. For example, when the intersection between variables are in a flat, horizontal line then it signifies that there is no relationship between the variables. This can be seen whereby when there is an increase in one unit on the x-axis, there will be no change of the variable in the y-axis.

Having a perfectly negative relationship, in other words, r = -1, in this type of relationship, for every one-unit increase in the horizontal axis, there is a consequent reduction of one unit in the vertical axis. In a perfect positive relationship, for every increase in one unit on the horizontal axis, there is a corresponding increase in the vertical axis, and for this, r = +1. One will realize that the relationship uses the term unit, whereby one gain on the x is associated with one unit increase on the y-axis. When looking graph that displays no relation, you will realize that r =0. This means that for every one increase in x, there is no corresponding change in the y hence no relationship. A graph showing no relationship will always be flat when a line is plotted horizontally or in a vertical direction. Bias in correlation can be avoided such no one will tend to think that a negative correlation is worse compared to a positive correlation. This can be curbed by squaring the correlation will show that the intensity of the relationship of two variables.

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Correlation coefficient
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They aid in depicting the actual degree of association of two variables . There are various types of correlation coefficients. This includes population correlation coefficients and sample correlation coefficients. The data’s correlation coefficient is utilized in measuring the degree of association between the variables, while the sample correlation coefficient is used to estimate the rho (p) and measure the strength of the linear relationship in the sample observations (Gogtay 2017) . To measure sample correlation, the following formula is applied:

With r= sample correlation coefficient, n= sample size, x = assigned digit for the independent variables, and y = value of the dependent variable.

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Features of p and r
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There are features of p and r that make them unique. Some of these characteristics consist unit-free, they exist between -1 to +1, where the one close to -1 is the stronger negative linear association while the one closer to 1 is the stronger positive linear relationship is when the correlation coefficient is more comparable to zero, then it means the linear relationship is relatively weak.

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What correlation analysis is concerned with
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The goal of correlation analysis is to quantify the extent of an association of two variables on a quantitative scale. It can be positive or negative, with positivity indicating correlation in one direction and a negative sign indicating correlation in the other way. However, a positive correlation does not necessarily imply one variable affects the other. In this case, none of the variables is manipulated as a section of the experiment. The data analytics’ objective is to measure the naturally occurring features, events or behaviors. The prober cannot make any conclusion concerning the resultant effect on one data set to the other but can determine the degree, the direction, and the magnitude of the association.

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References
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Apley, D. W., & Zhu, J. (2020). Visualizing the effects of predictor variables in black box supervised learning models.
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Journal of the Royal Statistical Society: Series B (Statistical Methodology)
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82
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(4), 1059-1086.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013).
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Applied multiple regression/correlation analysis for the behavioral sciences
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. Routledge.

Gogtay, N. J., & Thatte, U. M. (2017). Principles of correlation analysis.
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Journal of the Association of Physicians of India
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,
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65
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(3), 78-81.