Which component of a time series reflects long-term changes in the data over time?
Cyclical Variation
Trend
Irregularity
Seasonality
In factor analysis, what does the term 'communality' refer to?
The correlation between two factors
The proportion of variance in a variable explained by all factors
The uniqueness of a particular variable
The eigenvalue of a factor
The sampling distribution of a statistic is:
The distribution of the statistic across all possible samples of a given size.
The distribution of the statistic in a single random sample.
The same as the population distribution.
Always normally distributed.
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?
0.5
1
0.75
1.5
If a residual plot shows a funnel shape (increasing spread of residuals as the predicted value increases), what does this indicate?
Multicollinearity
Autocorrelation
Homoscedasticity
Heteroscedasticity
You want to compare the average heights of men and women in a population. Which hypothesis test would be most appropriate?
Chi-square test
One-sample t-test
Independent samples t-test
Paired t-test
When is ANOVA (Analysis of Variance) used instead of a t-test?
When comparing the means of three or more groups.
When comparing the means of two groups.
When analyzing the relationship between two categorical variables.
When comparing the variances of two groups.
In simple linear regression, what does a negative slope of the regression line indicate?
As the independent variable increases, the dependent variable decreases.
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable increases.
The relationship between the independent and dependent variables is non-linear.
What is the primary difference between simple exponential smoothing and double exponential smoothing?
Double exponential smoothing is used for stationary data, while simple exponential smoothing is used for non-stationary data.
Double exponential smoothing considers trend, while simple exponential smoothing does not.
Simple exponential smoothing uses a moving average, while double exponential smoothing uses an autoregressive model.
Simple exponential smoothing considers seasonality, while double exponential smoothing does not.
In residual analysis, what does a pattern in the residuals plot indicate?
The errors have constant variance.
There is no correlation between the variables.
The linear model is a good fit for the data.
The relationship between the variables may not be linear.