MATHS EXAM NOTES.docx - CHAPTER 1 – BIVARIATE DATA Residual value is the difference between the actual y Bivariate data analysis will determine if a

# MATHS EXAM NOTES.docx - CHAPTER 1 – BIVARIATE DATA...

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CHAPTER 1 – BIVARIATE DATA Bivariate data analysis will determine if a relationship or association exists between two variables. The explanatory variable (independent) is the one that explains or influences change in the response variable. The response variable (dependent) measures an outcome or study. It depends on the explanatory variable. - A significant change in proportion of percentages in the data indicates there is an association. A scatter plot can be used to graph two numerical variables. The explanatory variable goes on the x-axis and the response variable goes on the y-axis. When interpreting the scatter plot , discuss FORM (Linear, non linear, no relationship) , DIRECTION (Positive, negative) , STRENGTH (Strong, moderate, weak) - If there is a linear relationship between two variables, we can calculate the correlation coefficient ( r ) If r = 1 or -1, there is a perfect positive or perfect negative relationship If r is between +- 0.75 and 1, there is a strong relationship If r is between +- 0.5 and 0.75, there is a moderate relationship If r is between +-0.25 and 0.5, there is a weak relationship If r is between -0.25 and +0.25 there is no relationship When describing using r, state the type of relationship (F,D,S) and then say that the y variable should __ as the x variable __ *If two variables are correlated it doesn’t necessarily mean that a change in one causes a change in the other. There may be external factors causing the relationship. CHAPTER 2 – BIVARIATE DATA – FURTHER ANALYSIS The least squares regression line is y=ax + b. The equations should be written in terms of the variable names. - To interpret the y-intercept in the LSR line, we state “The y variable is “_” units when the x variable is zero units.” To interpret the gradient in the LSR line, we state “The y- variable increases/decreases by “_” units for every one unit increase in the x-variable.” To plot the least squares regression line , plot the y- intercept and then select an x value and substitute it into the LSR line equation to find a corresponding y value. The coefficient of determination ( r 2 ) tells us the percentage of variation in the dependent variable that can be explained by the independent variable, therefore determining how useful or appropriate a linear model is. When interpreting the coefficient of determination , state “(r 2 x 100)% of the variation in the response variable can be explained by the variation in the explanatory variable.” When using the least squares regression line to make predictions , it is either interpolation or extrapolation. Interpolation: prediction made within the original data Extrapolation: prediction made outside the original data therefore less reliable. Residual value is the difference between the actual y value - predicted y value.

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