11/19 - Correlation Coefficient & Linear Regression

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What is the correlation coefficient and what does it indicate?

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The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation.

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CCSS.HSS.ID.C.8

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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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CCSS.8.SP.A.2

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How do you interpret a negative correlation coefficient?

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A negative correlation coefficient indicates that as one variable increases, the other variable tends to decrease. The strength of the correlation is determined by the absolute value of the coefficient.

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CCSS.HSS.ID.B.5

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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 of the line, b is the y-intercept, y is the dependent variable, and x is the independent variable.

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CCSS.8.EE.B.5

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What does a strong positive correlation look like on a scatter plot?

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A strong positive correlation on a scatter plot appears as points that are closely clustered around a line that slopes upwards from left to right.

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CCSS.HSS.ID.B.5

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How do you calculate the slope (m) in a linear regression equation?

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The slope (m) in a linear regression equation can be calculated using the formula: m = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2), where N is the number of data points.

Tags

CCSS.8.EE.B.5

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

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The y-intercept (b) represents the value of the dependent variable (y) when the independent variable (x) is zero. It is the point where the regression line crosses the y-axis.

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CCSS.HSF.LE.B.5

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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 make predictions by substituting a value for the independent variable (x) into the equation to solve for the dependent variable (y).

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CCSS.HSF.IF.A.2

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What does it mean to round coefficients to the nearest hundredth in a linear regression equation?

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Rounding coefficients to the nearest hundredth means adjusting the numerical values of the coefficients to two decimal places for precision and clarity.

Tags

CCSS.8.EE.B.5

Front

How do you determine the strength of correlation from scatter plots?

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The strength of correlation from scatter plots can be determined by observing how closely the points cluster around a line. The closer the points are to forming a straight line, the stronger the correlation.

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CCSS.HSF-LE.A.1B