Preview_Scatterplots and Linear Regression

What is linear regression?

• A method used to calculate the mean of a dataset.

• A machine learning algorithm used to classify data into different categories.

• A technique used to analyze time series data.

• A statistical method used to model the relationship between a dependent variable and one or more independent variables.

What is the correlation coefficient?

• The correlation coefficient is a measure of the spread of data points around the mean.

• The correlation coefficient is a measure of the difference between two variables.

• The correlation coefficient is a measure of the probability of a relationship between two variables.

• The correlation coefficient is a statistical measure that measures the strength and direction of the linear relationship between two variables.

How is the line of best fit determined in a scatterplot?

• Correlation coefficient

• Interpolation

• Extrapolation

• Linear regression

What are residuals in the context of linear regression?

• The average of the observed and predicted values of the dependent variable.

• Differences between observed and predicted values of the dependent variable.

• The sum of the observed and predicted values of the dependent variable.

• The product of the observed and predicted values of the dependent variable.

How do you interpret scatterplots?

• Scatterplots are used to visualize the relationship between two variables.

• Scatterplots show the distribution of a single variable.

• Scatterplots are used to display categorical data.

• Scatterplots are only used for linear relationships.

What is the purpose of linear regression?

• The purpose of linear regression is to predict future outcomes.

• The purpose of linear regression is to determine causation between variables.

• The purpose of linear regression is to analyze categorical data.

• The purpose of linear regression is to model the relationship between variables.

What does a positive correlation coefficient indicate?

• As one variable decreases, the other variable also decreases.

• There is no relationship between the two variables.

• As one variable increases, the other variable also increases.

• As one variable increases, the other variable decreases.

What does a negative correlation coefficient indicate?

• As one variable increases, the other variable decreases.

• As one variable decreases, the other variable decreases.

• There is no relationship between the variables.

• As one variable increases, the other variable increases.

How are residuals calculated in linear regression?

• By subtracting the predicted values from the actual values of the dependent variable.

• By dividing the predicted values by the actual values of the dependent variable.

• By multiplying the predicted values with the actual values of the dependent variable.

• By adding the predicted values to the actual values of the dependent variable.

What are some limitations of using scatterplots and linear regression?

• Some limitations of using scatterplots and linear regression include assumption of linearity, sensitivity to outliers, non-independence of observations, inability to capture non-linear relationships, and inability to extrapolate beyond the range of observed data.

• Scatterplots and linear regression have no limitations.

• Scatterplots and linear regression are only applicable to small datasets.

• Scatterplots and linear regression cannot handle categorical variables.