#1
Which of the following correlation coefficients represents a perfect positive linear relationship?
#2
In a scatter plot, if the points tend to form a straight line sloping upwards from left to right, what type of correlation is likely present?
Positive correlation
Negative correlation
No correlation
Non-linear correlation
#3
Which of the following statements about correlation coefficients is correct?
Correlation coefficients range from -1 to 1
Correlation coefficients range from 0 to 100
Correlation coefficients range from -100 to 100
Correlation coefficients range from 0 to 1
#4
What is the purpose of a scatter plot in statistical analysis?
To display the distribution of a single variable
To visualize the relationship between two variables
To calculate the mean of a dataset
To perform hypothesis testing
#5
Which of the following is a measure of central tendency?
Standard deviation
Variance
Median
Range
#6
What is Pearson's correlation coefficient used for?
To measure the strength and direction of a linear relationship between two variables
To measure the spread of data points in a dataset
To calculate the mean of a dataset
To determine the mode of a dataset
#7
Which statistical test is used to determine if there is a significant association between two categorical variables?
Pearson's correlation coefficient
Chi-squared test
ANOVA
T-test
#8
What does the coefficient of determination (R-squared) measure?
The strength of association between two variables
The proportion of the variance in the dependent variable that is predictable from the independent variable
The accuracy of predictions made by a model
The average distance between data points and the regression line
#9
Which of the following statements about correlation is true?
Correlation implies causation
Correlation indicates a causal relationship between variables
Correlation does not imply causation
Correlation only occurs in linear relationships
#10
What is the purpose of regression analysis?
To measure the strength of association between two variables
To predict the value of a dependent variable based on one or more independent variables
To identify the cause-and-effect relationship between variables
To describe the central tendency of a dataset
#11
What does the slope of the regression line represent in linear regression?
The coefficient of determination
The coefficient of correlation
The change in the dependent variable for a one-unit change in the independent variable
The standard error of the estimate
#12
Which of the following statements about outliers is true?
Outliers always need to be removed from the dataset
Outliers can significantly affect statistical analyses
Outliers have no impact on statistical analyses
Outliers are only present in regression analysis
#13
What does the p-value represent in hypothesis testing?
The probability of making a Type I error
The probability of making a Type II error
The probability of observing the data given that the null hypothesis is true
The probability of rejecting the null hypothesis when it is true
#14
What is multicollinearity in regression analysis?
When there is a perfect positive correlation between predictor variables
When there is no correlation between predictor variables
When predictor variables are correlated with each other
When predictor variables are not related to the dependent variable
#15
What is the formula for calculating the slope (β) in simple linear regression?
(Σ(xy) - ΣxΣy) / (Σx^2 - (Σx)^2)
(ΣxΣy) / (Σx^2)
(Σxy) / (Σx^2)
(Σx^2) / (Σxy)
#16
What does the term 'heteroscedasticity' refer to in regression analysis?
The presence of outliers in the dataset
The assumption that the residuals are normally distributed
The unequal variance of residuals across levels of the independent variable
The perfect multicollinearity between predictor variables
#17
Which of the following is NOT an assumption of linear regression?
Linearity
Independence of residuals
Homoscedasticity
Normality of independent variables
#18
In regression analysis, what does the term 'collinearity' refer to?
The assumption that the residuals are normally distributed
The presence of outliers in the dataset
The perfect linear relationship between predictor variables
The assumption that the errors have constant variance