M4U8D2 Regression Lines and Residuals

Front

What is the Coefficient of Determination?

Back

The Coefficient of Determination is represented as r squared, indicating the proportion of variance in the dependent variable that can be explained by the independent variable.

Front

How do you calculate a residual?

Back

A residual is calculated as Observed - Predicted.

Front

What does the correlation coefficient represent?

Back

The correlation coefficient summarizes the direction and strength of the correlation between two variables.

Front

What is the value of the correlation coefficient, r, in a linear regression model?

Back

The correlation coefficient, r, indicates the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1.

Front

In a study predicting crop yield based on fertilizer, what is the response variable?

Back

The response variable is the yield of the crop.

Front

What does a positive correlation coefficient indicate?

Back

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

Front

What does a negative correlation coefficient indicate?

Back

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

Front

What is the purpose of a regression line?

Back

A regression line is used to model the relationship between two variables and to make predictions.

Front

What is the formula for a simple linear regression line?

Back

The formula for a simple linear regression line is y = a + bx, where 'a' is the y-intercept and 'b' is the slope.

Front

What does the slope of a regression line represent?

Back

The slope of a regression line represents the change in the response variable for each one-unit change in the explanatory variable.