Linear Regression

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What is Linear Regression?

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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 does a scatter plot represent in linear regression?

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A scatter plot represents the relationship between two quantitative variables, showing how one variable may be affected by another.

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How do you interpret a positive correlation in linear regression?

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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 linear regression context?

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

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What does it mean if there is no correlation in a scatter plot?

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No correlation means that there is no discernible relationship between the two variables; changes in one variable do not predict changes in the other.

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What is the formula for a linear regression equation?

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

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What does the slope (m) represent in a linear regression equation?

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The slope (m) represents the rate of change of the dependent variable (y) for each unit change in the independent variable (x).

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

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The y-intercept (b) is the value of the dependent variable (y) when the independent variable (x) is zero.

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How is the strength of a correlation measured in linear regression?

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The strength of a correlation is often measured using the correlation coefficient (r), which ranges from -1 to 1.

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What does an r value of 0.3 indicate about the correlation?

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An r value of 0.3 indicates a weak positive correlation between the two variables.