Scatter Plots and Line of Best Fit

Front

What is a scatter plot?

Back

A scatter plot is a graphical representation that displays the relationship between two quantitative variables, using dots to represent individual data points.

Front

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

Back

The line of best fit is a straight line that best represents the data on a scatter plot, indicating the general direction of the relationship between the variables.

Front

How do you determine the slope of a line of best fit?

Back

The slope of a line of best fit can be determined by calculating the change in the y-values divided by the change in the x-values (rise over run) between two points on the line.

Front

What is a residual in the context of regression analysis?

Back

A residual is the difference between the observed value and the predicted value from a regression model, indicating how far off the prediction was.

Front

What does a negative residual indicate?

Back

A negative residual indicates that the observed value is less than the predicted value, meaning the model overestimated the actual value.

Front

What is the purpose of a residual plot?

Back

A residual plot is used to assess the fit of a regression model by plotting the residuals on the y-axis against the predicted values or independent variable on the x-axis.

Front

What does it mean if a residual plot shows a random scatter of points?

Back

If a residual plot shows a random scatter of points, it suggests that the linear model is a good fit for the data, as there are no patterns in the residuals.

Front

How can you use a trend line to make predictions?

Back

A trend line can be used to make predictions by extending the line into the future or for values not present in the data set, allowing for estimation of y-values based on x-values.

Front

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

Back

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

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the value of y when x is equal to zero, indicating where the line crosses the y-axis.