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In statistics, the regression equation is used to find out the extent of the relationship between sets of data. It models the linear relationships and trends between variables, allowing us to explain or predict certain outcomes.
A regression line refers to the line of best fit for your data. It almost represents an average of where all your data points line up. In linear regression, the regression line is straight. In non-linear regression, the line is curved. Non-linear and linear data require different methods to model their relationship. Within this article, we will specifically explore linear regression and go over the steps required to arrive at a regression equation by hand. We will also explore the strengths and benefits of modelling the relationship between variables using regression analysis.
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Now that we’ve understood what the regression equation is, let’s take a look at the steps we can use to arrive at a regression equation by hand.
The regression equation takes the following form:
Y = the dependent variable(s)
X = the independent variable
b = the slope of the line
a = the y-intercept
Use the following steps to arrive at your regression equation:
The first step is to create a chart of your data. Arrange your data in a table, clearly outlining each variable separately.
The next step is to use the following equation to calculate your ‘a’ value, also known as the y-intercept.
Use the following equation to calculate your ‘b’ value, also known as the slope of the line.
Once you’ve found your ‘a’ and ‘b’ values, simply insert them into your equation (Y=a + bX) to arrive at your linear regression equation.
The following are a few strengths of regression analysis:
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The following are a few limitations of regression analysis:
A regression equation is used in statistics to reveal the degree of relation between sets of data. The equation can be used to model the relationship between the variables, allowing us to predict or explain the outcomes.
A regression line can be described as “the line of best fit” for a set of data. It represents an average of where all your data points line up.
A few limitations of regression analysis are;
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