Scatterplots and Lines of Best Fit

Front

What is a scatterplot?

Back

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

Front

What does the slope of a line represent in a scatterplot?

Back

The slope of a line in a scatterplot represents the rate of change between the two variables. A positive slope indicates a positive relationship, while a negative slope indicates a negative relationship.

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 scatterplot, showing the general direction of the data points.

Front

How do you determine the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive correlation look like in a scatterplot?

Back

A positive correlation in a scatterplot appears as a pattern where data points trend upwards from left to right.

Front

What does a negative correlation look like in a scatterplot?

Back

A negative correlation in a scatterplot appears as a pattern where data points trend downwards from left to right.

Front

What does no correlation mean in a scatterplot?

Back

No correlation means there is no discernible pattern in the data points; they are scattered randomly.

Front

How can you use a trend line to make predictions?

Back

You can use a trend line to predict values by extending the line and finding the corresponding value on the y-axis for a given x-value.

Front

What is the formula for the slope of a line of best fit in a scatterplot?

Back

The slope of a line of best fit can be calculated using the least squares method, which minimizes the sum of the squares of the vertical distances of the points from the line.

Front

What is the significance of the y-intercept in a line of best fit?

Back

The y-intercept is the value of y when x is zero; it indicates where the line crosses the y-axis and can provide context for the relationship.