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 as a straight line on a graph, typically in the form of the equation 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 in a linear model?

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 a positive slope?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, resulting in an upward trend on a graph.

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What is a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, resulting in a downward trend on a graph.

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What does a slope of zero indicate?

Back

A slope of zero indicates that there is no change in the dependent variable (y) as the independent variable (x) changes, resulting in a horizontal line on a graph.

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How can you determine if a scatter plot shows a linear relationship?

Back

A scatter plot shows a linear relationship if the points roughly form a straight line, either increasing or decreasing, without significant deviation from that line.

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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 equal to zero. It is the point where the line crosses the y-axis.

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

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

Front

What is the significance of the slope in real-world applications?

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The slope can represent various real-world relationships, such as speed (distance over time), cost per item, or any other rate of change between two quantities.

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What is the difference between a linear and a non-linear relationship?

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A linear relationship can be represented by a straight line, while a non-linear relationship cannot be represented by a straight line and may involve curves or other shapes.