The ________ is used to fit the regression line in a simple linear regression model.
- least squares method
- mean
- median
- mode
The least squares method is used to find the best-fitting line through the data points. This is done by minimizing the sum of the squares of the vertical distances of the points from the line.
In multiple linear regression, ________ is used to test the overall significance of the model.
- the Chi-square statistic
- the F-statistic
- the Z-statistic
- the t-statistic
In multiple linear regression, the F-statistic is used to test the overall significance of the model. This test checks the null hypothesis that all regression coefficients are zero against the alternative that at least one of them is not zero. If the F-statistic is significantly large and the corresponding p-value is small, we reject the null hypothesis, concluding that the regression model has some validity in predicting the outcome variable.
What is the primary purpose of conducting an ANOVA test?
- To calculate the standard deviation of a dataset
- To determine the mode of a set of data
- To find the correlation between two variables
- To test the equality of means among groups
The primary purpose of an ANOVA test is to compare the means of different groups and determine whether any of those means are significantly different from each other.
How is the confidence interval for a proportion calculated?
- nan
- p ± (z*√(p(1-p)/n))
- p ± z*(s/√n)
- p ± z*(σ/√n)
The confidence interval for a proportion is calculated using the formula: p ± (z*√(p(1-p)/n)), where p is the sample proportion, z is the z-score associated with the desired confidence level, and n is the sample size.
What is the relationship between Cramér's V and the Chi-square test?
- Cramér's V is the inverse of the Chi-square statistic
- Cramér's V is the square of the Chi-square statistic
- Cramér's V is the square root of the Chi-square statistic divided by the sample size and the minimum of rows and columns minus 1
- There is no relationship between Cramér's V and the Chi-square test
Cramér's V is a measure of association between two nominal variables and it is based on the Chi-square statistic. It is calculated as the square root of the Chi-square statistic divided by the sample size and the minimum of rows and columns minus 1.
What kind of data is suitable for the Kruskal-Wallis Test?
- Binary data
- Nominal data
- Normal data
- Ordinal or continuous data
The Kruskal-Wallis Test is suitable for ordinal or continuous data that is not normally distributed.
Why is interval estimation generally preferred over point estimation?
- Because it gives more accurate results
- Because it is easier to calculate
- Because it is less affected by outliers
- Because it provides a range of possible values rather than a single point
Interval estimation is generally preferred over point estimation because it provides a range of possible values rather than a single value. This range of values gives a better understanding of the uncertainty around the estimate, hence, it provides more information than a single point estimate.
Spearman's Rank Correlation is especially useful when the relationship between variables is ________, but not necessarily linear.
- Bimodal
- Monotonic
- Negative
- Positive
Spearman's Rank Correlation is especially useful when the relationship between variables is monotonic, but not necessarily linear. A monotonic relationship is one where the variables tend to change together, but not necessarily at a constant rate.
If the null hypothesis is true in ANOVA, the F-statistic follows a ________ distribution.
- Binomial
- Chi-Square
- F
- Normal
In ANOVA, if the null hypothesis is true, the F-statistic follows an F-distribution. The F-distribution is a probability distribution that is used most commonly in Analysis of Variance.
What does a Pearson Correlation Coefficient of 0 indicate?
- No correlation
- Perfect negative correlation
- Perfect positive correlation
- Weak positive correlation
A Pearson correlation coefficient of 0 indicates no correlation. This means that the variables are independent and there is no linear relationship between them.