Welcome to Regression Analysis. This topic is used extensively in ISC Maths, Statistics and in Engineering Mathematics. So here's giving you an idea of how to go about studying this chapter.

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There are a few free resources such as youtube videos here. Feel free to use them. In case you still need that extra help, you can contact me for online tutoring.

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The statistical method which helps us in estimating the value of one variable, given the other variable is called regression. To learn regression, you'll need to have an idea of Correlation , Covariance and standard deviation.  We can plot a scatter diagram for the data and then plot a smooth curve representing the data. This method is called curve fitting.

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There are two regression lines for two variables x and y. Firstly, we have the line of regression of y on x where y is the dependent variable and x is the independent variable. Next, we have the line of regression of x on y where x is the dependent variable and y is the independent variable.

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Basics of Regression analysis-Lesson 1

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We also have two regression coefficients, the regression coefficient of x on y which is also the slope of the regression line of x on y.  Next, we have the regression coefficient of y on x which is the slope of the regression equation of y on x. There are multiple methods of calculating the regression coefficients. 

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You can calculate the regression coefficients from the two regression equations or there are separate formulas to calculate them. There are also formulas which show the relation between the regression coefficients, the correlation coefficient and the standard deviations of the variables. Note the the correlation coefficient r takes the same sign as the regression coefficients.

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Learn more about Regression Analysis

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The correlation coefficient r is the geometric mean of the two regression coefficients. The point of intersection of the two regression lines is the arithmetic mean of the variables. The two regression lines coincide if and only if the correlation coefficient r is plus or minus one.

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If the correlation coefficient is equal to zero, then the lines of regression are parallel to the coordinate axes. You can also calculate the acute angle between the two lines of regression.

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All these topics and more will be taught in my online classes. Learn formulas, concept based questions, case study based questions and basic problem solving skills. Share this with high school mathematics students.