Use Linear Models to Make Predictions

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What is a linear model?

Back

A linear model is a mathematical representation of the relationship between two variables that can be expressed with a linear equation, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

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What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

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How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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What is a scatter plot?

Back

A scatter plot is a graph that shows the relationship between two quantitative variables by displaying data points on a two-dimensional plane.

Front

How can a trend line be used in a scatter plot?

Back

A trend line is a straight line that best represents the data points in a scatter plot. It can be used to make predictions about the relationship between the variables.

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What does it mean if the slope of a line is positive?

Back

If the slope of a line is positive, it means that as the independent variable (x) increases, the dependent variable (y) also increases.

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What does it mean if the slope of a line is negative?

Back

If the slope of a line is negative, it means that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the formula for a linear equation in slope-intercept form?

Back

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

Front

How do you interpret the slope of a linear model in a real-world context?

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The slope of a linear model indicates how much one variable is expected to change for each unit increase in another variable, providing insight into the strength and direction of their relationship.