An autoregressive model (AR) uses ______ values of the time series to predict future values.
Random
Future
Average
Past
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?
Cannot be determined
0.3
0.7
0.5
Which component of a time series reflects long-term changes in the data over time?
Irregularity
Trend
Cyclical Variation
Seasonality
When would you use a paired t-test instead of an independent t-test?
When comparing the means of two independent groups.
When comparing the means of the same group before and after a treatment.
When comparing the means of three or more groups.
When comparing the means of two groups with unequal variances.
A company manufactures light bulbs. The probability that a bulb is defective is 0.05. If you choose 3 bulbs at random, what is the probability that at least one bulb is defective?
0.999875
0.143
0.000125
0.857
In exponential smoothing, a higher value of the smoothing parameter (alpha) gives _______ weight to recent observations.
Higher
Equal
Lower
Zero
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
All residuals clustered around zero
Residuals consistently increasing with increasing values of the independent variable
A curved pattern in the residuals
Randomly scattered residuals
What is the primary purpose of inferential statistics?
To organize and clean raw data.
To make generalizations about a population based on a sample.
To describe and summarize data.
To visually represent data using graphs and charts.
In PCA, what does a scree plot help determine?
The presence of multicollinearity
The amount of variance explained by each variable
The correlation between principal components
The optimal number of principal components to retain
In residual analysis, what does a pattern in the residuals plot indicate?
The linear model is a good fit for the data.
There is no correlation between the variables.
The errors have constant variance.
The relationship between the variables may not be linear.