Correlation & Regression Skills

Calculate the correlation coefficient between two variables when given the data points.

• The correlation coefficient can be greater than 1

• The correlation coefficient between two variables can range from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

• The correlation coefficient is calculated by dividing the sum of the data points

• The correlation coefficient is always 0 for any data points

Interpret a scatterplot showing a strong positive correlation.

• The scatterplot will show points clustered closely around a horizontal line.

• The scatterplot will show points clustered closely around a line that slopes upwards from left to right.

• The scatterplot will show points scattered randomly with no clear trend.

• The scatterplot will show points clustered closely around a line that slopes downwards from left to right.

Understand the coefficient of determination and its significance in regression analysis.

• R^2 is significant in regression analysis as it helps assess the goodness of fit of the model and the strength of the relationship between the independent and dependent variables.

• R^2 is only applicable to linear regression

• R^2 is insignificant in regression analysis

• R^2 measures the accuracy of the model predictions

Calculate the correlation coefficient between two variables when given the data points.

• A correlation coefficient of 0 means the variables are perfectly related

• Correlation coefficient is always positive

• The correlation coefficient between two variables can range from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.

• The correlation coefficient can be greater than 1

Interpret a scatterplot showing a strong negative correlation.

• The scatterplot will show a positive correlation.

• The scatterplot will show a downward sloping pattern from left to right.

• The scatterplot will show no pattern or relationship between the variables.

• The scatterplot will show an upward sloping pattern from left to right.

Understand the coefficient of determination and its relationship to the strength of a regression model.

• R-squared measures the accuracy of the regression model predictions

• A coefficient of determination of 0.5 indicates a weak regression model

• R-squared is not related to the strength of a regression model

• R-squared is a measure of how well the regression model fits the observed data, with values closer to 1 indicating a stronger fit.

Calculate the correlation coefficient between two variables when given the data points.

• Correlation coefficient is always equal to the slope of the regression line

• The correlation coefficient between two variables can range from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

• A correlation coefficient of 0 means the variables are perfectly negatively related

• The correlation coefficient can be greater than 1

Interpret a scatterplot showing no correlation between two variables.

• The scatterplot shows no correlation between the two variables.

• The scatterplot shows a strong negative correlation between the two variables.

• The scatterplot shows a strong positive correlation between the two variables.

• The scatterplot shows a linear relationship between the two variables.

Apply regression analysis to analyze the relationship between independent and dependent variables.

• Apply regression analysis to analyze the relationship between independent and dependent variables.

• Ignore the relationship between variables

• Use classification analysis instead

• Apply clustering analysis

Identify outliers in a set of data points and evaluate their influence on regression results.

• Calculate Z-scores for data points, identify outliers, and assess their impact on regression results by comparing model performance with and without outliers.

• Apply the interquartile range method to detect outliers

• Use the mean of the data points to identify outliers

• Ignore outliers completely in the regression analysis