Linear Regression & Scatterplots

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What is Linear Regression?

Back

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

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What is a Scatterplot?

Back

A scatterplot is a graphical representation of two variables where each point represents an observation. It helps to visualize the relationship between the variables.

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What does a positive correlation indicate in a scatterplot?

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A positive correlation indicates that as one variable increases, the other variable also tends to increase.

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What does a negative correlation indicate in a scatterplot?

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A negative correlation indicates that as one variable increases, the other variable tends to decrease.

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What is the equation of a line in linear regression?

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The equation of a line in linear regression is typically expressed as y = mx + b, where m is the slope and b is the y-intercept.

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How do you interpret the slope in a linear regression equation?

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The slope (m) in a linear regression equation indicates the change in the dependent variable (y) for each one-unit increase in the independent variable (x).

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What is the y-intercept in a linear regression equation?

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The y-intercept (b) is the value of y when the independent variable (x) is zero. It represents the starting point of the line on the y-axis.

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How can you use a linear regression equation to make predictions?

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You can use a linear regression equation to predict the value of the dependent variable (y) by substituting a value for the independent variable (x) into the equation.

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What is the purpose of a trend line in a scatterplot?

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A trend line in a scatterplot summarizes the relationship between the variables and helps to make predictions based on the data.

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What does it mean if a scatterplot shows no correlation?

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If a scatterplot shows no correlation, it means there is no discernible relationship between the two variables; changes in one variable do not predict changes in the other.