Linear Regression Review

Front

What does 'least-squares' mean in the context of linear regression?

Back

It refers to minimizing the sum of the squares of the residuals.

Front

What does the slope of the least squares line represent?

Back

It indicates how much the response variable (e.g., income) changes for each one-unit increase in the explanatory variable (e.g., hours worked).

Front

What is the ideal appearance of a residual plot?

Back

A residual plot should appear random with no discernible pattern.

Front

What does a correlation coefficient of r = -0.01 imply?

Back

It implies that a linear model is not a good fit for the data.

Front

How would you describe a strong negative correlation in a graph?

Back

A strong negative correlation means that as one variable increases, the other variable tends to decrease significantly.

Front

What is a residual in linear regression?

Back

A residual is the difference between the observed value and the predicted value from the regression model.

Front

What does a positive slope in a least squares regression line indicate?

Back

It indicates that as the explanatory variable increases, the response variable also increases.

Front

What is the purpose of a residual plot?

Back

To assess the fit of a regression model by checking for patterns in the residuals.

Front

What does a correlation coefficient of r = 0 indicate?

Back

It indicates no correlation between the two variables.

Front

What is the formula for the least squares regression line?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.