In simple linear regression, what does a negative slope of the regression line indicate?
As the independent variable increases, the dependent variable decreases.
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable increases.
The relationship between the independent and dependent variables is non-linear.
Which of the following is NOT an assumption of a two-sample t-test?
The variances of the two groups are equal.
The data points within each group are independent.
The two groups are dependent on each other.
The data in each group are normally distributed.
What does a residual in regression analysis represent?
The intercept of the regression line
The correlation between the independent and dependent variables
The difference between the observed value and the predicted value of the dependent variable
The slope of the regression line
A Chi-square test is most appropriate for analyzing which type of data?
Categorical data
Normally distributed data
Continuous data
Time series data
When is Spearman's rank correlation a more appropriate measure of association than Pearson's correlation?
When outliers are not present in the data
When the relationship between variables is perfectly linear
When the variables are measured on an interval or ratio scale and normally distributed
When the relationship between variables is non-linear but monotonic
What is the purpose of using a correlation matrix in multivariate statistics?
To visualize the distribution of residuals in regression
To identify outliers in a dataset
To assess the strength and direction of linear relationships between pairs of variables
To determine the optimal number of factors in factor analysis
In PCA, what does a scree plot help determine?
The presence of multicollinearity
The amount of variance explained by each variable
The optimal number of principal components to retain
The correlation between principal components
What does a Pearson correlation coefficient of -0.9 suggest about the relationship between two variables?
Strong negative linear relationship
Weak positive linear relationship
No linear relationship
Strong positive linear relationship
Which of the following is NOT an assumption of a t-test?
The data is normally distributed.
The variances of the groups being compared are equal (for independent samples t-test).
The data is categorical.
The observations are independent.
The lifetime of a certain electronic component follows an exponential distribution with a mean of 10,000 hours. What is the probability that a randomly selected component lasts less than 5,000 hours?
0.5
0.3935
0.25
0.6321