What are the assumptions made while applying ANOVA?
- Independence, Homogeneity of variance, Non-linearity
- Linearity, Independence, Equal Variance
- Normality, Homogeneity of variance, Independence
- Normality, Linearity, Independence
While applying ANOVA, the following assumptions are made: Normality (data is normally distributed), Homogeneity of variance (variance among the groups is approximately equal), Independence (the observations are independent of each other).
What is interval estimation in inferential statistics?
- The process of calculating the standard deviation of a population
- The process of determining the mode of a population
- The process of estimating the mean of a population
- The process of providing a range of values for an unknown population parameter
Interval estimation in inferential statistics is a method by which a range of values is provided that is likely to contain the population parameter. Instead of a single value, it provides an interval of estimates making it more flexible and informative than point estimation.
How do non-parametric tests treat data points?
- They analyze only the maximum and minimum data values
- They analyze ranks rather than actual data values
- They analyze the median of the data set only
- They ignore outliers in the data set
Non-parametric tests treat data points by analyzing their ranks rather than their actual values. This makes non-parametric tests less sensitive to extreme values and makes them a good choice when dealing with skewed data or data with many outliers.
The Central Limit Theorem states that the sampling distribution of the sample means approaches a ________ distribution as the sample size gets larger, regardless of the shape of the population distribution.
- Poisson
- binomial
- normal
- uniform
The Central Limit Theorem is a fundamental theorem in statistics that states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, no matter what the shape of the population distribution. This outcome is significant because it enables us to make statistical inferences about the population mean based on the distribution of sample means.
Why is it important to check the assumptions of a multiple linear regression model?
- To ensure the validity of the model
- To increase the complexity of the model
- To increase the number of observations
- To reduce the R-squared value
Checking the assumptions of a multiple linear regression model (like linearity, independence, normality, and homoscedasticity) is crucial to ensure the validity of the model and its estimates. Violations of these assumptions can lead to biased or inefficient estimates, and inferences made from such models could be misleading.
In what situations can the use of stepwise regression for model selection be problematic?
- When the true model is non-linear.
- When there are too few predictor variables.
- When there are too many predictor variables.
- When there is no multicollinearity.
Stepwise regression assumes a linear relationship between the predictors and the response. It might be problematic when the true model is non-linear, leading to incorrect inferences.
The conditional probability of A given B is denoted as ________.
- P(A + B)
- P(A / B)
- P(A B)
- P(A ∩ B)
The conditional probability of A given B is denoted as P(A
What is the primary goal of random sampling?
- To always select the same individuals
- To ensure that every member of the population has an equal chance of being selected
- To select individuals who are likely to give the desired results
- To select the individuals who are easiest to reach
The primary goal of random sampling is to ensure that every member of the population has an equal chance of being selected. This helps to reduce bias and increase the likelihood that the sample is representative of the population, which makes the results more valid and generalizable.
_______ regression is a method used to handle multicollinearity by adding a degree of bias to the regression estimates.
- Logistic
- Polynomial
- Ridge
- Simple linear
Ridge regression handles multicollinearity by introducing a degree of bias to the regression estimates, reducing their variance, and making them more reliable.
What are the assumptions made by the Spearman’s Rank Correlation test?
- The data is continuous and the relationship is monotonic
- The data is normally distributed and linear
- The data is ordinal and the relationship is linear
- The data is ordinal or continuous and the relationship is monotonic
The Spearman’s Rank Correlation test assumes that the variables are ordinal or continuous and that the relationship between them is monotonic. It does not require the relationship to be linear or the data to be normally distributed.