How can one adjust for multicollinearity in a multiple linear regression model?
- By adding interaction terms
- By increasing the sample size
- By removing one of the correlated variables or combining the correlated variables
- By transforming the dependent variable
To adjust for multicollinearity in a multiple linear regression model, one of the common strategies is to remove one of the highly correlated independent variables or to combine the correlated variables.
How does the effect size relate to the power of a t-test?
- Effect size has no relation to the power of a test
- Larger effect sizes are associated with higher power
- Larger effect sizes are associated with lower power
- nan
The effect size is the magnitude of the difference between groups. Larger effect sizes are easier to detect and are associated with higher power in a t-test.
What is the value of the probability of an impossible event?
- 0
- 0.5
- 1
- The probability is undefined
By definition, the probability of an impossible event is 0. This is because the measure of probability assigns 0 to events that cannot occur and 1 to events that are certain to occur.
_________ is a condition in which the error term in a regression model is correlated with itself.
- Autocorrelation
- Homoscedasticity
- Multicollinearity
- Underfitting
Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. In the context of a regression analysis, it refers to the condition when the error term (residuals) in a regression model is correlated with itself.
How is the F-statistic calculated in an ANOVA test?
- It is the difference between between-group variance and within-group variance
- It is the ratio of between-group variance to within-group variance
- It is the ratio of within-group variance to between-group variance
- It is the sum of between-group variance and within-group variance
In an ANOVA test, the F-statistic is calculated as the ratio of the between-group variance (mean sum of squares between groups) to the within-group variance (mean sum of squares within groups). A larger F-statistic implies a greater degree of difference between the group means.
What is the difference between excess kurtosis and kurtosis?
- Excess kurtosis is always greater than kurtosis
- Excess kurtosis is always less than kurtosis
- Excess kurtosis is kurtosis minus 3
- There is no difference between excess kurtosis and kurtosis
The difference between kurtosis and excess kurtosis comes down to a constant. Excess kurtosis is simply kurtosis minus 3. The "3" comes from the kurtosis of a normal distribution which is 3. Hence, excess kurtosis refers to kurtosis in relation to a normal distribution.
What is the role of the 'R-squared' value in a multiple linear regression model?
- It represents the correlation between the dependent and independent variables
- It represents the error term in the regression model
- It represents the proportion of variance in the dependent variable that is predictable from the independent variables
- It represents the total variance in the dependent variable
The 'R-squared' value, also known as the coefficient of determination, in a multiple linear regression model represents the proportion of variance in the dependent variable that can be predicted from the independent variables. It ranges from 0 to 1, where a higher value indicates a better fit of the model.
What is the support of a continuous random variable?
- The highest and lowest value of the variable
- The mean value of the distribution
- The set of values that have non-zero probability
- The variance of the distribution
The support of a random variable is the set of values in the range of the variable that have non-zero probability. For a continuous random variable, it's the set of values over which the probability density function is non-zero.
In simple linear regression, the assumption that the variance of the errors is constant across all levels of the independent variables is known as ________.
- autocorrelation
- heteroscedasticity
- homoscedasticity
- multicollinearity
In statistics, homoscedasticity (or homoskedasticity) is the assumption that the variance of the errors is constant across all levels of the independent variables. This is an important assumption in regression models, including simple linear regression.
How does sample size affect the accuracy of a statistic?
- Larger samples lead to less accurate statistics
- Larger samples lead to more accurate statistics
- Sample size does not affect the accuracy of a statistic
- The relationship between sample size and statistic accuracy is unpredictable
Larger samples tend to lead to more accurate statistics. The reason is that as we increase the sample size, the sample mean gets closer to the population mean, reducing the standard error. In other words, larger samples provide a better estimate of the population parameters, leading to more accurate and reliable results. However, this doesn't mean larger samples are always feasible or more effective, as they require more resources and time.