least squares regression line

Front

What is the least squares regression line?

Back

The least squares regression line is a statistical method used to determine the line of best fit for a set of data points by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line.

Front

What does a correlation coefficient (r) of 0.8 indicate?

Back

A correlation coefficient (r) of 0.8 indicates a strong positive linear relationship between two variables.

Front

What does it mean if two variables are correlated?

Back

If two variables are correlated, it means that there is a statistical relationship between them, indicating that changes in one variable are associated with changes in the other.

Front

What does random scatter in the residuals indicate about a regression model?

Back

Random scatter in the residuals indicates that a linear model is appropriate for the data, suggesting that the model captures the relationship well without systematic errors.

Front

What does a correlation coefficient near 1 or -1 signify?

Back

A correlation coefficient near 1 signifies a strong positive linear relationship, while a coefficient near -1 signifies a strong negative linear relationship between two variables.

Front

How does changing the units of measurement for x or y affect the correlation coefficient?

Back

Changing the units of measurement for x or y does not change the correlation coefficient; it remains the same regardless of the units used.

Front

What is a residual plot?

Back

A residual plot is a graphical representation of the residuals (the differences between observed and predicted values) plotted against the independent variable or predicted values, used to assess the fit of a regression model.

Front

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

Back

If a residual plot shows a pattern, it suggests that the linear regression model may not be appropriate for the data, indicating that a non-linear model might be a better fit.

Front

What is the purpose of the line of best fit in a scatter plot?

Back

The purpose of the line of best fit in a scatter plot is to summarize the relationship between two variables, providing a predictive model for estimating values.

Front

What is the significance of the slope in a regression line?

Back

The slope of a regression line indicates the change in the dependent variable for each one-unit change in the independent variable, reflecting the strength and direction of the relationship.