In multiple linear regression, the __________ test is used to test if a group of variables contributes to the prediction of the response.
- Chi-square test
- F-test
- T-test
- Z-test
The F-test is used in multiple regression to test whether at least one of the predictors' regression coefficient is not equal to zero. In other words, it tests whether the predictors are significant in explaining the response variable.
How does the sample size relate to the power of a test?
- It depends on the effect size
- Larger sample sizes decrease power
- Larger sample sizes increase power
- Sample size has no influence on power
Larger sample sizes increase the power of a test because they provide more data, reducing the influence of random error and making it easier to detect an effect if one exists. This is why researchers often aim to recruit as large a sample as possible, within the constraints of their resources.
If two events A and B are mutually exclusive, the probability of both occurring is _______.
- 0
- 0.5
- 1
- The probability is undefined
If two events A and B are mutually exclusive, the probability of both occurring is 0. Mutually exclusive events cannot occur at the same time.
How does the Law of Large Numbers impact the calculation of probabilities?
- It changes the probability of an event based on previous outcomes.
- It doesn't affect the calculation of probabilities.
- It guarantees that the experimental probability gets closer to the theoretical probability as the number of trials increases.
- It states that all probabilities must be equal.
The Law of Large Numbers impacts the calculation of probabilities by asserting that as the number of trials (or observations) increases, the experimental probabilities will get closer and closer to the theoretical (or true) probabilities. It gives validity to the notion of probability in practical applications.
The Sign Test is based on the direction of the _________ between pairs.
- differences
- medians
- ranks
- signs
The Sign Test is based on the direction of the differences between pairs.
How does the Breusch-Pagan test check for heteroscedasticity in residuals?
- By comparing the variance of residuals
- By examining the correlation of residuals
- By plotting residuals against fitted values
- By regressing the squared residuals on the predictors
The Breusch-Pagan test checks for heteroscedasticity by regressing the squared residuals on the predictors. If the predictors explain a significant amount of variance in the squared residuals, the test concludes that heteroscedasticity is present.
___________ occurs when changes in one variable are associated with changes in another variable, but one does not necessarily cause the other.
- Causation
- Correlation
- Covariation
- Regression
Correlation occurs when changes in one variable are associated with changes in another variable. It's important to remember that correlation does not imply causation. Just because two variables move together, it does not mean that one variable's movement is causing the other's.
How does the variability of the population affect the width of a confidence interval?
- Higher variability decreases the width of the confidence interval
- Higher variability increases the width of the confidence interval
- The relationship between variability and the width of the confidence interval is unpredictable
- Variability has no effect on the width of the confidence interval
Higher variability in the population increases the width of the confidence interval. When data points are spread out more (higher variability), there is more uncertainty about where the true population parameter lies, leading to a larger standard error and thus a wider confidence interval.
In a scatter plot, a __________ trend suggests a positive relationship between variables.
- Downward
- Horizontal
- Upward
- Vertical
In a scatter plot, an upward trend suggests a positive relationship between the variables. This means as one variable increases, the other variable also increases.
What is the null hypothesis in an ANOVA test?
- The means of all groups are different
- The means of all groups are equal
- The variances of all groups are different
- The variances of all groups are equal
The null hypothesis in an ANOVA test is that the means of all groups are equal. If the p-value obtained from the ANOVA test is less than the significance level, the null hypothesis is rejected, implying that there is a significant difference between at least two of the group means.