The bin width (and thus number of categories or ranges) in a histogram can dramatically affect the ________, skewness, and appearance of the histogram.
- Interpretation
- Mean
- Median
- Mode
The bin width and the number of bins in a histogram can dramatically affect the interpretation, skewness, and overall appearance of the histogram. This is because the choice of bin size can influence the level of detail visible in the histogram, potentially either obscuring or highlighting certain patterns in the data.
In PCA, if two variables are similar, they will have _______ loadings on the same component.
- high
- low
- opposite
- random
In PCA, if two variables are similar or highly correlated, they will have high loadings on the same component. This is because PCA identifies the directions (Principal Components) in which the data varies the most, and similar variables will contribute to this variance in the same way.
What is the impact of heteroscedasticity on a multiple linear regression model?
- It affects the linearity of the model
- It affects the normality of the residuals
- It causes multicollinearity
- It invalidates the statistical inferences that could be made from the model
Heteroscedasticity, or non-constant variance of the error term, can invalidate statistical inferences that could be made from the model because it violates one of the assumptions of multiple linear regression. This could lead to inefficient estimation of the regression coefficients and incorrect standard errors, which in turn affects confidence intervals and hypothesis tests.
What is the impact of data transformation on the decision to use non-parametric tests?
- A suitable data transformation may make it possible to use a parametric test
- Data transformation always leads to non-parametric tests
- Data transformation always makes data normally distributed
- Data transformation does not affect the choice between parametric and non-parametric tests
A suitable data transformation may make it possible to use a parametric test instead of a non-parametric test. Transformations can help to stabilize variances, normalize the data, or linearize relationships between variables, allowing for the use of parametric tests that might have more statistical power.
If two events are independent, what is the conditional probability of one given the other?
- 0
- 1
- Equal to the probability of the given event
- Undefined
If two events are independent, the conditional probability of one event given the other is simply the probability of the event itself. This is because in independent events, the occurrence of one event does not affect the occurrence of the other event.
In what situation could a "Type II" error occur during hypothesis testing?
- When the alternative hypothesis is false
- When the null hypothesis is false but not rejected
- When the null hypothesis is rejected
- When the null hypothesis is true
A Type II error, also known as a false negative, occurs when the null hypothesis is false, but we fail to reject it.
Principal Component Analysis (PCA) is a dimensionality reduction technique that projects the data into a lower dimensional space called the _______.
- eigen space
- feature space
- subspace
- variance space
PCA is a technique that projects the data into a new, lower-dimensional subspace. This subspace consists of principal components which are orthogonal to each other and capture the maximum variance in the data.
The range of a dataset is sensitive to _______.
- Mean
- Median
- Mode
- Outliers
The range of a dataset is sensitive to outliers. Because the range is calculated as the difference between the maximum and minimum values, an outlier (an extremely high or low value) can greatly increase the range.
The type of factor analysis in which the researcher assumes that all variance in the observed variables is common variance is known as _______ factor analysis.
- common factor
- confirmatory
- exploratory
- principal component
The type of factor analysis in which the researcher assumes that all variance in the observed variables is common variance is known as common factor analysis.
The Kruskal-Wallis Test is used to compare ________ independent samples.
- four
- three
- three or more
- two
The Kruskal-Wallis Test is used to compare three or more independent samples. It's an extension of the Mann-Whitney U Test for more than two groups.