Exploring Algebra and Statistics

What is the result of multiplying a 2x3 matrix by a 3x2 matrix?

• The result is a 3x3 matrix.

• The result is a 1x2 matrix.

• The result is a 2x1 matrix.

• The result is a 2x2 matrix.

Define the term 'statistical inference'.

• Statistical inference refers to the process of organizing data into tables.

• Statistical inference is the method of calculating the mean of a sample.

• Statistical inference is the process of drawing conclusions about a population based on sample data.

• Statistical inference is the collection of data from a population.

Which Python library is commonly used for data manipulation and analysis?

• Matplotlib

• NumPy

• Scikit-learn

• Pandas

What is the formula for the slope in linear regression?

• m = (Σx^2 - Σy^2) / N

• m = (Σy - Σx) / N

• m = (Σxy) / (Σx + Σy)

• m = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2)

Explain the difference between mean and median.

• The mean is the average, while the median is the middle value in a sorted list.

• The median is the average of all values.

• The mean is always greater than the median.

• The mean is the middle value in a sorted list.

What is the determinant of a 2x2 matrix [[a, b], [c, d]]?

• ad + bc

• ad - bc

• ab - cd

• ac + bd

What is a confidence interval in statistics?

• A confidence interval is a single value that represents the population mean.

• A confidence interval is a method to calculate the exact population parameter.

• A confidence interval is a fixed number that does not change with sample size.

• A confidence interval is a range of values that estimates the true population parameter with a specified level of confidence.

Name a Python library that is used for statistical analysis.

• SciPy

• Matplotlib

• Pandas

• NumPy

What is the purpose of the intercept in a linear regression model?

• The intercept represents the slope of the regression line.

• The intercept indicates the starting point of the regression line on the y-axis.

• The intercept is used to calculate the correlation coefficient.

• The intercept shows the variance of the dependent variable.

How do you calculate the variance of a dataset?

• Variance = (Σ(xi - mean)²) / N for population, or Variance = (Σ(xi - mean)²) / (N - 1) for sample.

• Variance = (Σ(xi - median)²) / N

• Variance = Σ(xi) / N

• Variance = (Σ(xi + mean)²) / N