The ________ measures the proportion of the variance in the dependent variable that is predictable from the independent variables in a multiple linear regression.
- Correlation coefficient
- F-statistic
- R-squared value
- Regression coefficient
The R-squared value, also known as the coefficient of determination, measures the proportion of the variance in the dependent variable that can be predicted from the independent variables in a multiple linear regression. It ranges from 0 to 1, with 1 indicating perfect prediction.
What are the consequences of violating the assumption of independence in a Chi-square test for goodness of fit?
- It can cause the test to be biased, leading to incorrect conclusions
- It can cause the test to be overly sensitive to small differences
- It can cause the test to have a lower power
- It can cause the test to incorrectly reject the null hypothesis
Violating the assumption of independence in a Chi-square test for goodness of fit can lead to biased results and incorrect conclusions. This is because the test assumes that the observations are independent, and this assumption is necessary for the test's validity.
A point estimate is a single value that serves as an estimate of the ________.
- Median
- Population parameter
- Sample
- Variable
A point estimate is a single value used as an estimate of a population parameter. The sample mean, for instance, might be used as a point estimate of the population mean.
ANOVA assumes that all populations being compared have the same ________.
- All of these
- Mean
- Sample size
- Variance
One of the assumptions of ANOVA is the assumption of homogeneity of variances, which means that all populations being compared have the same variance.
What is the primary purpose of Principal Component Analysis (PCA)?
- To calculate the mean of data
- To classify data
- To reduce dimensionality of data
- To visualize data
The primary purpose of PCA is to reduce the dimensionality of data while maintaining as much information as possible. It transforms the data into a new, lower-dimensional set of variables that are uncorrelated and that explain the maximum possible amount of variance in the data.
The measure of dispersion that is the square root of the variance is known as the _______.
- Mean
- Median
- Range
- Standard Deviation
The standard deviation is the square root of the variance. It measures the average distance between each data point and the mean. Like the variance, it expresses the dispersion of data around the mean, but unlike the variance, its units are the same as the original data, making it easier to interpret.
What is the purpose of a Chi-square test for goodness of fit?
- To compare the means of two groups
- To compare the variance of two groups
- To determine the correlation between two variables
- To test if a data set follows a given theoretical distribution
The Chi-square test for goodness of fit is used to test whether the observed data fits a specific distribution. It compares the observed data with the values that would be expected under the theoretical distribution.
What does the slope of the regression line represent in simple linear regression?
- It represents the change in the dependent variable for a one-unit change in the independent variable
- It represents the error term
- It represents the independent variable
- It represents the strength of the correlation
The slope of the regression line in simple linear regression represents the change in the dependent variable for a one-unit change in the independent variable. It quantifies the strength and direction of the linear relationship between the two variables.
The ________ probability in Bayes' theorem is the revised probability of an event occurring after taking into account new information.
- joint
- marginal
- posterior
- prior
In Bayes' theorem, the posterior probability is the revised probability of an event occurring after taking into account new evidence.
What does a 95% confidence interval mean?
- That 95% of the population is within the interval
- That 95% of the sample data lies within the interval
- That the interval captures the true population parameter 95% of the time
- That there is a 95% chance that the interval contains the mean
A 95% confidence interval means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95% of the cases.