Scatter Plots & Interpreting Linear Models

Front

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 axis.

Front

What does the line of best fit represent in a scatter plot?

Back

The line of best fit represents the trend of the data points in a scatter plot, indicating the general direction of the relationship between the variables.

Front

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

Back

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

Front

What does a positive correlation in a scatter plot indicate?

Back

A positive correlation indicates that as one variable increases, the other variable also tends to increase.

Front

What does a negative correlation in a scatter plot indicate?

Back

A negative correlation indicates that as one variable increases, the other variable tends to decrease.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

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

Back

The slope represents the rate of change between the two variables; for example, in a baseball context, it could represent the average number of hits per at-bat.

Front

What does it mean if there is no correlation in a scatter plot?

Back

No correlation means that there is no discernible relationship between the two variables; changes in one do not predict changes in the other.

Front

How do you determine the equation of a line of best fit from a scatter plot?

Back

To determine the equation, you can use statistical methods such as linear regression to find the best-fitting line that minimizes the distance from all data points.