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Non-linear structure - Coggle Diagram
Non-linear structure
Correlation- statistical measure that describe the extent to which two variables change together. Example: as a study hours increases exam scores tend to increase indicating a positive correlation.
SP( Computation Formula) an alternative way to calculate the sum of products using means and deviations. Example: SP=nE(x_iy_i)
Outliers data points that are significantly different from others in datatset. Example: in a set of test scores a score of 100 when most scores are around 60.
Correlation Matrix a table showing the correlation coefficients between multiple variables. Example a matrix showing correltions betwen height, weight, and age.
Restricted Range a limited range of data that can affect the correltion coefficient often underestimating the true relationship. Examples stduying only college students from one university may limit the range of scores.
SP( definitional formula) the formula used to caluate the sum of products in correlation analysis ( Example SP= e(x_i*y_i)
Coefficient of Determination the square of the Pearson correlation coefficient representing the proportion of variance in one varible explained by another. Example an r2 of 0.64 indicates 64% of the variability in Y is explained by x.
Spearman Correlation - non parametric measure of rank correltion, assessing how well the reltionship between two variables can be describe by a montonic function.
Monntonic Relationship- a reltionship where variables tend to move in the same or opposite direction, but not necessarily at a constant rate. Example the relationship between age and income where income generally increases with age.
Point-biserial correlation - a correlation between a continuous variable and a binary variable. Example correlation between gender male/ female and test scores.
Dichotomous Variable or Binomial Variable- a variable with only tow possible values. Example yes or no repsonses or passe or failed outcomes.
Phi-coefficient- measure of association for two binary variables. Examples correlation between smoking status smoker /non smoker and lung disease y/N
Linear Equation- equation that models a striaight line relationship between variables. example_y=2x+5
Slope- the rate at which y changes for a unit change in x in a linear equations. Example y= 2x+5 the slope is 2
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Pearson Correlation- a measure of linear correlation between two variable ranging from -1 or 1. Example: Calculating the Pearson correlation coefficient between hours studied and exam scores.
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Linear Relationship reltionship between two variables that can be represented with a straight line. Example: the lreationship between distance traveled and time at constant speed.
Sum of Product- SP the sum of the products of paried data points, oftern used in correlation calculations. Examples: for data points (x1,y1) (x2, y2) SP= x1y+x2y2+
Scatter Plot a graph that displays points representing that values of two different variables, showing their relationships. Example: plotting students study hours against thie test scorces to see if there's a pattern.
Positive Correlation a relationship where both variables increase or decease together. Example height and weight tend to have positive correlations taller people often weight more.
Negative Correlation a relationsip where one variable increases while the other decreases.Example the amount of time spent watching tv and grades more tv watching might correlate with lower grades.
Perfection Correlation- correlation where the variable move perfect ly in sync with a correlation coefficient of 1 or -1. Examples: two variables that always increase or decrease together in a predictable way.
Envelope a curve that encloses a set a data points in line the context of regression to show the boundary of data. Example the upper and lower bounds of a scatter plot showing the maximum and minimum values.