Residual Plots

Front

What is a residual in the context of regression analysis?

Back

A residual is the difference between the actual value and the predicted value from a regression model, calculated as: residual = actual - predicted.

Front

What does the correlation coefficient (r) indicate in a dataset?

Back

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).

Front

How do you interpret a correlation coefficient of 0.976?

Back

A correlation coefficient of 0.976 indicates a very strong positive linear relationship between the two variables being analyzed.

Front

What is the formula for calculating a residual?

Back

The formula for calculating a residual is: residual = actual - predicted.

Front

What does a scatterplot represent in regression analysis?

Back

A scatterplot visually represents the relationship between two quantitative variables, showing how one variable is affected by the other.

Front

What is the purpose of a line of best fit in a scatterplot?

Back

The line of best fit is used to summarize the relationship between the variables in a scatterplot, providing a predictive model for estimating values.

Front

What does it mean if the residual plot shows a random pattern?

Back

A random pattern in a residual plot suggests that the linear regression model is appropriate for the data, indicating that the model's assumptions are met.

Front

What does it indicate if a residual plot shows a curved pattern?

Back

A curved pattern in a residual plot suggests that a linear model may not be appropriate, indicating that a non-linear model might better fit the data.

Front

How can you estimate values using a line of best fit?

Back

You can estimate values by substituting the independent variable into the linear regression equation derived from the line of best fit.

Front

What is the significance of rounding values in regression equations?

Back

Rounding values in regression equations helps simplify the equation for practical use while maintaining a reasonable level of accuracy.