Scatter Plot Correlation DE Stat Review

Front

What is the equation of a linear regression model used to predict a dependent variable based on an independent variable?

Back

A linear regression model is typically expressed in the form y = mx + b, where y is the dependent variable, m is the slope, x is the independent variable, and b is the y-intercept.

Front

What does the residual represent in a regression analysis?

Back

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

Front

How do you calculate the residual for a given data point?

Back

Residual = Observed value - Predicted value.

Front

What is the Coefficient of Determination (r²) in a scatterplot?

Back

The Coefficient of Determination (r²) measures the proportion of variance in the dependent variable that can be explained by the independent variable.

Front

What does a high r² value indicate about the relationship between two variables?

Back

A high r² value indicates a strong relationship between the independent and dependent variables, meaning that the model explains a large portion of the variance.

Front

What is extrapolation in the context of regression analysis?

Back

Extrapolation is the process of predicting values of the dependent variable for independent variable values that fall outside the range of the observed data.

Front

What does a correlation coefficient (r) of 0.987 indicate about the relationship between two variables?

Back

A correlation coefficient of 0.987 indicates a strong positive linear relationship between the two variables.

Front

What is the significance of a residual plot in regression analysis?

Back

A residual plot helps to assess the fit of a regression model; patterns in the residuals can indicate whether a linear model is appropriate.

Front

What conclusion can be drawn if a residual plot shows a random scatter of points?

Back

If a residual plot shows a random scatter of points, it suggests that a linear model is a good fit for the data.

Front

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

Back

If a residual plot shows a clear pattern, it indicates that the linear model may not be appropriate for the data.