Math Notes.docx - Bivariate Data Male Female Totals Residuals Party A 215 42 257 Party B 104 61 165 Totals 319 103 422 Refers to the vertical distance

Math Notes.docx - Bivariate Data Male Female Totals...

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Bivariate Data Party A Party B Totals Male 215 104 319 Female 42 61 103 Totals 257 165 422 Row percentages Party A Party B Totals Male 67% 33% 100% Female 41% 59% 100% Column percentages Party A Party B Male 84% 63% Female 16% 37% Total 100% 100% Explanatory variable : the variable used to explain or predict a difference in the response variable Response variable : also called the dependent variable Scatterplots Positive : from bottom left to top right Negative : from top left to bottom right Strong : how close the points follow a linear pattern 1 2 3 4 0 1 2 3 4 5 6 7 8 9 No. people No. people Eg: The graph above is a strong positive graph Correlation coefficient/determination R : measures the direction and strength of a linear relationship. Says that ‘X’ is a good predicter of ‘Y’ R^2 : measures the percentage variation in both variable with respect to each other Euler and planar graphs v + f = e + 2 If Euler’s rule works, then the graph can be drawn as planar Planar : no edges in a graph cross over each other Residuals Refers to the vertical distance between a data point and line of best fit Linear model only appropriate if residuals are in random order How to calculate 1) Statistics 2) Enter numbers 3) Calc 4) Regression 5) Linear regression 6) Copy residuals to list 3 Sequences Arithmetic : each term is found by adding or subtracting/linear growth Arithmetic sequeces Explicit T n = a + ( n 1 ) ×d Recursive T n + 1 = T n + d ,T 1 = a Where; A : the first term in the sequence N : the ‘nth’ term in the sequence D : the common difference Examples Recursive,T n + 1 = T n + 5, where T 1 = 10 OR Explicit ,T n = 10 ( n 1 ) × 5 Geometric : each term is found by multiplying or dividing/exponential growth Geometric sequences Explicit T n = ar n 1 Recursive T n + 1 = T n ×r ,T 1 = a Where; r : the common ratio A : the first term N : the ‘nth’ term in the sequence Examples Recursive,T n + 1 = T n × 4, whereT 1 = 5 OR
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Explicit ,T n =( 5 )( 4 ) n 1 Types of graphs Simple graph : does not contain loops or multiple edges Connected graph : a possible path between every vertex Directed graph : the is directed by the use of arrows Weighted graph : edges on a graph that have been assigned a numerical value Tree
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