In ANOVA, what does the F-statistic represent?
The ratio of between-group variance to within-group variance.
The difference between the smallest and largest group means.
The probability of observing the data if all group means were equal.
The correlation coefficient between the independent and dependent variables.
In simple linear regression, what does the slope of the regression line represent?
The strength of the relationship between the variables
The change in the dependent variable for a one-unit change in the independent variable
The point where the regression line crosses the y-axis
The average value of the dependent variable
A high R² value in a regression analysis always indicates a good fit of the model. Is this statement true or false?
False
True
You're playing a game where you flip a coin. Heads, you win $10. Tails, you lose $5. What is the expected value of playing this game?
$2.50
-$2.50
$0.00
$5.00
What is the purpose of using a correlation matrix in multivariate statistics?
To visualize the distribution of residuals in regression
To identify outliers in a dataset
To determine the optimal number of factors in factor analysis
To assess the strength and direction of linear relationships between pairs of variables
Which distribution is often used to model the time between events that occur independently and at a constant average rate?
Normal Distribution
Binomial Distribution
Poisson Distribution
Exponential Distribution
What is a key assumption of autoregressive models?
The data has a constant mean and variance over time.
The data is free from outliers and missing values.
The time series data exhibits strong seasonality.
There is no correlation between past and future values.
An event has three possible outcomes: A, B, and C. You know P(A) = 0.2 and P(B) = 0.3. What is the value of P(C) according to the law of total probability?
0.5
0.7
0.3
Cannot be determined
What is the null hypothesis in a Chi-square test of independence?
The two variables are independent.
The means of the two groups are equal.
The two variables are dependent.
The variances of the two groups are equal.
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
Chi-square test
Independent samples t-test
Paired t-test
One-sample t-test