__________ in multiple linear regression refers to the proportion of the variance in the dependent variable that is predictable from the independent variables.
- Beta coefficient
- F-statistic
- R-squared
- T-statistic
R-squared is a statistical measure in regression models that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables.
How does the Spearman’s Rank Correlation test handle ties in data ranks?
- Assigns the maximum rank to ties
- Assigns the minimum rank to ties
- Averages the tied ranks
- Ignores the tied ranks
The Spearman’s Rank Correlation test handles ties in data ranks by averaging the ranks. For example, if two values tie for a place in the ranking, they are assigned a rank equal to the average of those places.
What are the ways to check the assumptions of an ANOVA test?
- By calculating the F-statistic
- By calculating the mean and variance of each group
- By checking normality of residuals, homogeneity of variance, and independence of observations
- By conducting post-hoc tests
The assumptions of an ANOVA test can be checked by: 1. Checking the normality of residuals using a normal probability plot or a statistical test like the Shapiro-Wilk test; 2. Checking the homogeneity of variance using a Levene's test or Bartlett's test; 3. Checking the independence of observations which usually pertains to the study design (random sampling, random assignment).
If the occurrence of A does not affect the occurrence of B, we say A and B are ________.
- Dependent
- Independent
- Joint
- Mutually exclusive
If the occurrence of A does not affect the occurrence of B, we say A and B are independent. This is a key concept in probability theory where the occurrence of one event does not change the probability of another.
What is the purpose of a Z-test?
- To assess the relationship between categorical variables
- To calculate the correlation between two variables
- To compare sample and population means when the population standard deviation is known
- nan
A Z-test is used to compare the mean of a sample to the mean of a population when the population standard deviation is known. It's not used to calculate correlations or assess relationships between categorical variables.
Can Pearson's Correlation Coefficient be used with non-linear relationships?
- No, never
- Yes, always
- Yes, but it may not provide meaningful results
- Yes, but only if the relationship is monotonic
While you can technically compute a Pearson correlation coefficient for non-linear relationships, it may not provide meaningful results. The Pearson correlation measures the degree of a linear relationship between variables, and does not fully capture the dynamics of a non-linear relationship. In such cases, Spearman's rank correlation or other non-parametric correlations may be more appropriate.
The degrees of freedom for a Chi-square test for a contingency table with r rows and c columns is (r-1)*(c-1), otherwise known as ________ degrees of freedom.
- dependent
- independent
- joint
- multicollinearity
The degrees of freedom for a Chi-square test for a contingency table with r rows and c columns is calculated as (r-1)*(c-1). These are also known as independent degrees of freedom as they depend on the number of independent ways that the data can vary.
How is a probability distribution defined?
- It is the average value of a dataset
- It is the highest and lowest value of a dataset
- It is the likelihood of each possible outcome of a random variable
- It is the spread of possible values in a dataset
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.
A value of 0 in Pearson's Correlation Coefficient means there's no ________ correlation between the two variables.
- linear
- negative
- perfect
- visible
A value of 0 in Pearson's Correlation Coefficient means there's no linear correlation between the two variables. However, it's important to note that this doesn't necessarily mean there is no relationship at all, it could be that the relationship is nonlinear.
What is the purpose of non-parametric statistical methods?
- To analyze data without making assumptions about the population distribution
- To make the calculation process more complex
- To provide less accurate results
- To use less data in the analysis
Non-parametric statistical methods are used to analyze data without making assumptions about the population distribution. These tests are based on differences in medians or ranks rather than differences in means.
What does the interquartile range in a box plot represent?
- The middle 50% of the data
- The range of the top 25% of the data
- The range within one standard deviation from the mean
- The total range of the dataset
The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range within which the central half of the values fall and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
What strategies can be employed to reduce both Type I and Type II errors?
- Decrease sample size, use a more lenient significance level
- Decrease sample size, use a more stringent significance level
- Increase sample size, use a more lenient significance level
- Increase sample size, use a more stringent significance level
Increasing the sample size makes the test more sensitive, reducing both Type I and Type II errors. Similarly, a more stringent significance level (lower α) reduces the chance of a Type I error. However, it's important to note that decreasing Type I error probability often leads to an increase in Type II error probability, and vice versa. This is known as the Type I/Type II tradeoff.