Linear Regression and Correlation Coefficient

What is the correlation coefficient?

• A statistic that measures the strength and direction of a linear association between two quantitative variables.

• A measure of the average of a set of values.

• A statistic that indicates the degree of variation in a dataset.

• A method for calculating the mean of two variables.

What does a strong negative correlation look like on a scatter plot?

• A strong negative correlation shows points that are closely clustered around a line that slopes downwards.

• A strong negative correlation shows points that are randomly scattered with no discernible pattern.

• A strong negative correlation shows points that are clustered around a horizontal line.

• A strong negative correlation shows points that are evenly distributed across the scatter plot.

How can you determine the strength of a correlation?

• By the value of the correlation coefficient, where values closer to 1 or -1 indicate stronger correlations.

• By the number of data points in the dataset.

• By the mean of the dataset.

• By the range of the dataset.

What type of correlation is shown when the scatter plot slopes upwards from left to right?

• Negative correlation

• No correlation

• Positive correlation

• Inverse correlation

What does a correlation coefficient of r=1 indicate?

• A correlation coefficient of r=1 indicates a perfect positive linear correlation between the two variables.

• A correlation coefficient of r=1 indicates no correlation between the two variables.

• A correlation coefficient of r=1 indicates a perfect negative linear correlation between the two variables.

• A correlation coefficient of r=1 indicates a weak positive correlation between the two variables.

What is a scatter plot?

• A type of bar graph that shows comparisons among discrete categories.

• A graph that displays values for typically two variables for a set of data.

• A circular chart divided into sectors that represent proportions.

• A line graph that shows trends over time.

What does a weak positive correlation look like on a scatter plot?

• A weak positive correlation shows points that are tightly clustered around a horizontal line.

• A weak positive correlation shows points that are loosely clustered around a line that slopes upwards.

• A weak positive correlation shows points that are randomly scattered with no discernible pattern.

• A weak positive correlation shows points that are tightly clustered around a line that slopes downwards.

What does a correlation coefficient of r=0 indicate?

• A correlation coefficient of r=1 indicates a perfect positive correlation.

• A correlation coefficient of r=-1 indicates a perfect negative correlation.

• A correlation coefficient of r=0 indicates no correlation between the two variables.

• A correlation coefficient of r=0.5 indicates a moderate positive correlation.

What does a correlation coefficient of r=2 indicate?

• A correlation coefficient of r=2 is not possible, as the correlation coefficient must be between -1 and 1.

• A correlation coefficient of r=2 indicates a perfect positive correlation.

• A correlation coefficient of r=2 indicates a perfect negative correlation.

• A correlation coefficient of r=2 indicates no correlation.

What is the range of the correlation coefficient?

• From 0 to 1

• From -1 to 1

• From -0.5 to 0.5

• From -2 to 2