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 is a scatter plot?

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A scatter plot is a graphical representation of two variables, showing the relationship between them by displaying data points on a Cartesian plane.

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What does the line of best fit represent in a scatter plot?

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The line of best fit represents the trend in the data, showing the average relationship between the variables and helping to make predictions.

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How do you interpret the slope of a linear regression line?

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The slope indicates the change in the dependent variable for each one-unit change in the independent variable.

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What is the equation of a line in slope-intercept form?

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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What is the purpose of predicting values using a trend line?

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The purpose is to estimate unknown values based on the established relationship between the variables in the data set.

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What does it mean if the correlation coefficient is close to 1 or -1?

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A correlation coefficient close to 1 indicates a strong positive linear relationship, while a coefficient close to -1 indicates a strong negative linear relationship.

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

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The y-intercept is the value of the dependent variable when the independent variable is zero, providing a starting point for the line.

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How can you determine the best fit line from a set of data points?

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The best fit line can be determined using methods like the least squares method, which minimizes the sum of the squares of the vertical distances of the points from the line.

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What is an outlier in the context of linear regression?

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An outlier is a data point that significantly deviates from the trend established by the other data points, potentially affecting the accuracy of the regression model.