Which of the following sampling techniques is most likely to introduce bias?
Stratified random sampling
Simple random sampling
Systematic sampling
Convenience sampling
In factor analysis, what does the term 'communality' refer to?
The eigenvalue of a factor
The uniqueness of a particular variable
The proportion of variance in a variable explained by all factors
The correlation between two factors
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.
As the sample size increases, the standard error of the mean:
Increases
Decreases
Stays the same
Cannot be determined
What is the range of possible values for the coefficient of determination (R²)?
Depends on the data
-1 to 1
-∞ to +∞
0 to 1
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
There is a 95% probability that the true population mean falls between 60 and 80.
We are 95% confident that the sample mean falls between 60 and 80.
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
In PCA, what does a scree plot help determine?
The amount of variance explained by each variable
The optimal number of principal components to retain
The presence of multicollinearity
The correlation between principal components
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
A curved pattern in the residuals
Randomly scattered residuals
Residuals consistently increasing with increasing values of the independent variable
All residuals clustered around zero
When is ANOVA (Analysis of Variance) used instead of a t-test?
When comparing the means of two groups.
When comparing the means of three or more groups.
When analyzing the relationship between two categorical variables.
When comparing the variances of two groups.
Which component of a time series reflects long-term changes in the data over time?
Irregularity
Cyclical Variation
Trend
Seasonality