How does the least squares method work in the context of simple linear regression?
- It maximizes the sum of the residuals
- It maximizes the sum of the squared residuals
- It minimizes the sum of the residuals
- It minimizes the sum of the squared residuals
In the context of simple linear regression, the least squares method works by minimizing the sum of the squared residuals (the differences between the observed and predicted values). This approach ensures that the regression line is the best fit to the data.
The term ________ refers to variability within each group being compared in ANOVA.
- Between-group variance
- Total variance
- Within-group variance
- nan
Within-group variance refers to variability within each group being compared in ANOVA. It represents the variation due to differences within individual groups.
In factor analysis, the relationship between each variable and the underlying factor is called a _______.
- factor correlation
- factor covariance
- factor loading
- factor variance
In factor analysis, the relationship between each variable and the underlying factor is called a factor loading.
What happens to the width of a confidence interval as the confidence level increases?
- It decreases
- It fluctuates unpredictably
- It increases
- It stays the same
The width of a confidence interval increases as the confidence level increases. A higher confidence level means that you want to be more sure that you are capturing the true population parameter, which requires a wider interval.
What is the Central Limit Theorem and how does it relate to point and interval estimation?
- It implies that every data set is symmetrically distributed, which affects the reliability of point and interval estimations
- It suggests that all data has a central tendency and this affects the point and interval estimations
- It suggests that as sample size increases, the distribution of sample means approaches a normal distribution, which affects how we estimate population parameters
- It suggests that every large enough dataset is normally distributed, which is the foundation of point and interval estimations
The Central Limit Theorem states that when you have a sufficiently large sample, the distribution of the sample mean approximates a normal distribution, regardless of the shape of the population distribution. This allows us to make inferences about the population parameters using the sample mean and the standard error, which form the basis of point and interval estimation.
An event that cannot possibly occur has a probability of ________.
- -1
- 0
- 0.5
- 1
An event that cannot possibly occur is said to be impossible and has a probability of 0. This is in line with the definition of probability as a measure that takes values between 0 and 1, inclusive.
Bayes' theorem combines our prior knowledge about an event with evidence from data to provide a ________ probability.
- joint
- marginal
- posterior
- prior
The theorem combines our prior knowledge (the prior probability) and evidence (the likelihood) to provide a new, updated probability of an event (the posterior probability).
What are the components of a confidence interval?
- The population mean, the margin of error, and the level of confidence
- The population mean, the sample size, and the standard error
- The sample mean, the margin of error, and the level of confidence
- The sample mean, the population size, and the standard deviation
A confidence interval is composed of three parts: a point estimate (the sample mean), a margin of error (which depends on the standard error and the Z-value or T-value), and the level of confidence (which indicates the probability that the interval estimate contains the population parameter).
What does it mean when we say a non-parametric test makes fewer assumptions about the data distribution?
- The data distribution must be known
- The data does not have to follow a specific distribution, such as normal
- The data must be normally distributed
- The data must be uniformly distributed
When we say a non-parametric test makes fewer assumptions about the data distribution, we mean that the data does not have to follow a specific distribution, such as the normal distribution. Non-parametric tests are distribution-free tests and make no assumption about the probability distribution of the variables.
The Pearson's Correlation Coefficient measures the ________ between two variables.
- causal relationship
- linear correlation
- percentage similarity
- rank
Pearson's Correlation Coefficient measures the linear correlation between two variables. It quantifies the degree to which two variables are related to each other.