When is Spearman's rank correlation a more appropriate measure of association than Pearson's correlation?
When the variables are measured on an interval or ratio scale and normally distributed
When the relationship between variables is perfectly linear
When the relationship between variables is non-linear but monotonic
When outliers are not present in the data
A Chi-square test is used to:
Analyze the variance within and between groups.
Analyze the relationship between two categorical variables.
Compare the means of two groups.
Determine if a sample mean is significantly different from a known population mean.
What is the primary purpose of inferential statistics?
To make generalizations about a population based on a sample.
To describe and summarize data.
To organize and clean raw data.
To visually represent data using graphs and charts.
In multiple regression, what does a high variance inflation factor (VIF) indicate?
Heteroscedasticity in the residuals
Low multicollinearity among predictor variables
A good fit of the regression model
High multicollinearity among predictor variables
What is a key assumption of autoregressive models?
There is no correlation between past and future values.
The data is free from outliers and missing values.
The data has a constant mean and variance over time.
The time series data exhibits strong seasonality.
Let X be a random variable representing the number of heads when you toss a fair coin three times. What is the variance of X?
0.75
0.5
1
1.5
What does an R-squared value of 0.80 indicate?
80% of the variation in the dependent variable is explained by the independent variable.
The correlation between the variables is 0.80.
20% of the variation in the dependent variable is explained by the independent variable.
The slope of the regression line is 0.80.
Which of the following is an example of a non-parametric inferential statistical test?
z-test
t-test
ANOVA
Chi-square test
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
0.25
0.3125
0.6875
In ANOVA, what does the F-statistic represent?
The ratio of between-group variance to within-group variance.
The correlation coefficient between the independent and dependent variables.
The difference between the smallest and largest group means.
The probability of observing the data if all group means were equal.