Stats Quiz

What does the line of least squares in statistics represent?

• The line that maximizes the distances of all points from it

• The line that best fits the data according to the least squares criterion

• The line connecting all the data points without any error

• The line that passes through the origin only

Pearson's correlation coefficient measures the strength and direction of what kind of relationship between two variables?

• Non-linear

• Linear

• Exponential

• Logarithmic

Which of the following values of Pearson's correlation coefficient indicates the strongest possible negative linear relationship between two variables?

• 0

• 0.5

• -0.5

• -1

In the context of angular distance, what does a 0-degree angle between two vectors indicate about their relationship?

• They are orthogonal to each other

• They are perfectly negatively correlated

• They are perfectly positively correlated

• They are completely uncorrelated

What is the primary purpose of using the line of least squares in data analysis?

• To classify data into different categories

• To predict the value of a dependent variable based on the value of an independent variable

• To calculate the mean of the dataset

• To find the median value of the dataset

Which of the following is NOT a property of Pearson's correlation coefficient?

• It ranges from -1 to 1

• It is unaffected by changes in the scale of measurement

• It can be used for categorical data

• It measures the strength of a linear relationship

What does an angular distance of 180 degrees between two vectors signify?

• They are orthogonal to each other

• They are perfectly positively correlated

• They are perfectly negatively correlated

• They are completely uncorrelated

In the calculation of the line of least squares, what is minimized?

• The sum of the squares of the y-coordinates of the data points

• The sum of the squares of the residuals

• The sum of the residuals

• The product of the x and y coordinates of the data points

Which of the following scenarios is most suitable for using Pearson's correlation coefficient?

• To measure the relationship between gender and reading preference

• To measure the relationship between height and weight

• To measure the relationship between nationality and income

• To measure the relationship between hair color and IQ score

Angular distance is often used in which of the following fields?

• Literature analysis

• Vector space models in machine learning

• Historical research

• Political science