use linear models to make predictions

Front

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.

Front

What does the slope of a line represent in a linear model?

Back

The slope represents the rate of change between the two variables; it indicates how much one variable changes for a unit change in the other variable.

Front

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

Back

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

Front

What is a line of best fit?

Back

A line of best fit is a straight line that best represents the data on a scatter plot, used to make predictions.

Front

How can you use a trend line to make predictions?

Back

You can use the trend line to estimate the value of one variable based on the value of another variable.

Front

What is a scatter plot?

Back

A scatter plot is a graph that shows the relationship between two quantitative variables, with points representing individual data points.

Front

What does it mean if a scatter plot shows a linear relationship?

Back

It means that the data points can be approximated by a straight line, indicating a consistent relationship between the two variables.

Front

What is the purpose of making predictions with linear models?

Back

The purpose is to estimate unknown values based on known data, helping in decision-making and forecasting.

Front

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

Back

The y-intercept is the value of y when x is zero; it represents the starting point of the line on the y-axis.

Front

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

Back

The slope can be interpreted as the change in the dependent variable for each unit increase in the independent variable.