What is the range of possible values for the coefficient of determination (R²)?
0 to 1
-1 to 1
-∞ to +∞
Depends on the data
A moving average model is best suited for forecasting time series data with which characteristic?
Significant outliers
A constant mean
Strong seasonality
High volatility
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
Which of the following is NOT a key assumption of the Central Limit Theorem?
The population has a finite mean and variance.
The samples are independent and randomly selected.
The population distribution is normal.
The sample size is sufficiently large (generally n ≥ 30).
If the variance of a random variable is 9, what is its standard deviation?
9
81
18
3
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
$5.00
$0.00
In factor analysis, what does the term 'communality' refer to?
The eigenvalue of a factor
The correlation between two factors
The proportion of variance in a variable explained by all factors
The uniqueness of a particular variable
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
0.5
0.6875
0.25
0.3125
A random variable follows a uniform distribution between 0 and 10. What is the probability that the variable takes a value between 3 and 7?
0.3
0.7
0.4
The lifetime of a certain electronic component follows an exponential distribution with a mean of 10,000 hours. What is the probability that a randomly selected component lasts less than 5,000 hours?
0.6321
0.3935