Correlation and Regression

The most frequent strategies for examining the relationship between two quantitative variables are correlation and regression.

Correlation analysis determines whether two measurement variables are related and quantifies the relationship’s degree. At the same time, regression seeks to represent the relationship as an equation. For example, in the case of patients who attend an emergency department (ED), we could utilise correlation and regression. It would help us check if there is a link between age and urea level and if urea level can be anticipated for a given age. 

Here is a selection of important multiple-choice questions with answers to help you understand and learn the topic better. 

1. Which one of the following statements about the correlation coefficient is correct?
2. 1. The correlation coefficient is unaffected by scale changes.
   2. Both the change of scale and the change of origin have no effect on the correlation coefficient. 
   3. The correlation coefficient is unaffected by the change of origin.
   4. The correlation coefficient is affected by changes of origin and scale.

 Answer: option C.

2. Choose the correct option concerning the correlation analysis between 2 sets of data. 
3. 1. Multiple correlations is a correlational analysis comparing two sets of data.
   2. A partial correlation is a correlational analysis comparing two sets of data.
   3. A simple correlation is a correlational analysis comparing two sets of data.
   4. None of the preceding.

Answer: option C.

3. The slope of the regression line of Y on X is also referred to as the:
4. 1. Regression coefficient of X on Y
   2. The correlation coefficient of X on Y
   3. Regression coefficient of Y on X
   4. Correlation coefficient of Y on X.

Answer: option C.

4. Which of the assertions below is the least accurate?

1. 1. When outliers are present in the data series, correlation is a more reliable or relevant measure. 
   2. Two variables having a significant nonlinear relation can still have a relatively low correlation. 
   3. Correlation among two variables can emerge from their relationship with a third variable rather than a direct relationship between them.
   4. None of the preceding.

Answer: option A.

5. Choose the least likely assumption of a classic normal linear regression model?

1. 1. The independent variable and the dependent variable have a linear relationship.
   2. The independent variable is normally distributed. 
   3. There is no randomness in the independent variable.
   4. None of the preceding.

Answer: option B.

6. Which one of the below statements regarding the regression line is correct?

1. 1. The prediction equation is another name for a regression line.
   2. A regression line is also referred to as the line of the average relationship. 
   3. The estimating equation is another name for a regression line.
   4. All of the above.
   5. None of the preceding. 

Answer: option D.

7. The correlation coefficient is?

1. 1. The square of the coefficient of determination
   2. Can never be negative
   3. The square root of the coefficient of determination.
   4. The same as r square

Answer: option C.

8. The correlation for the values of two variables moving in the same direction is

1. 1. Perfect positive
   2. Negative
   3. Positive
   4. No correlation.

Answer: option C.

9. Who suggested the mathematical approach for determining the magnitude of a linear relationship between two variables, such as X and Y? 

1. 1. Ya Lun Chou
   2. Croxton and Cowden
   3. Karl Pearson
   4. Spearman.

Answer: option C.

10. Who introduced the term ‘regression’?

1. 1. Karl Pearson
   2. R.A Fischer
   3. Croxton and Cowden
   4. Francis Galton.

Answer: option D.

11. The correlation coefficient describes

1. 1. Only magnitude
   2. Both magnitude and direction
   3. Only direction
   4. None of the preceding options.

Answer: option B.

12. Which of the given plots is suitable for testing the linear relationship between a dependent and independent variable?

1. 1. Barchart
   2. Scatter plot
   3. Histograms
   4. All of the above.

Answer: option B.

13. Choose the method(s) that doesn’t have a closed-form solution for its coefficient?

1. 1. Lasso
   2. Ridge regression
   3. Both Lasso and Ridge
   4. None of the given options.

Answer: option A. 

14. The correlation for the values of two variables moving in the opposite direction is

1. 1. Positive
   2. Negative
   3. Nonlinear
   4. Linear
   5. No correlation.

Answer: option B. 

15. Which of the given statements concerning type two errors is correct

1. 1. Accepting a correct hypothesis is a type two error.
   2. Accepting an incorrect hypothesis is referred to as a type two error.
   3. Rejecting a correct hypothesis is a type two error.
   4. Rejecting an incorrect hypothesis is referred to as a type two error.

Answer: option B.

16. What is the value of the correlation coefficient if the coefficient of determination is 0.81?

1. 1. Must be positive
   2. 0.656
   3. Either +0.9 or -0.9
   4. Must be negative

Answer: option C.

17. Regression modelling is a statistical tool for building a mathematical equation depicting how

1. 1. One explanatory and one or above response variables are related
   2. There is a link between one response variable and one or many explanatory variables
   3. Several explanatory and response variables are related
   4. All of the above are correct.

Answer: option B.

18. Which of the below statements concerning two regression coefficients’ arithmetic mean is correct?

1. 1. It is greater than the correlation coefficient.
   2. It is less than that of the correlation coefficient.
   3. It is equal to or greater than the correlation coefficient.
   4. It’s equal to the correlation coefficient.

Answer: option A. 

19. Which of the given strategies helps provide the prediction mechanism by analysing the relationship between two variables?

1. 1. Regression
   2. Standard error
   3. Correlation
   4. None of the preceding. 

Answer: option A.

20. For correlation analysis, which of the given assertions is true?

1. 1. It is a multivariate analysis
   2. It is a bivariate analysis
   3. It is a univariate analysis
   4. It is both bivariate and univariate analysis. 

Answer: option C.

21. Choose the correct example for positive correlation.

1. 1. Weight and income
   2. Price and demand
   3. The repayment period and EMI
   4. Income and expenditure

Answer: option D.

22. Which of the below options isn’t a required assumption regarding the error term ε in the least-squares regression?

1. 1. The error term’s variance is the same for all values of x.
   2. The error term’s values are independent.
   3. The error term’s expected value is one.
   4. The error term follows a normal distribution.

Answer: option C.

23. Choose the right option for the types of correlation.

1. 1. Linear and nonlinear
   2. Positive and negative
   3. Simple, multiple, and partial
   4. None of the above
   5. All of the above.

Answer: option D. 

24. What is the variable’s name in regression analysis that is used to explain a change in the outcome of an experiment or a natural process?

1. 1. The predictor variable
   2. The x variable
   3. The independent variable
   4. None of the above
   5. All of the above from a to c.

Answer: option E.

25. For a correlation of determination equal to 1, what is the value of the correlation coefficient?

1. 1. It can be any value between +1 and -1
   2. It must be equal to -1
   3. It can be either +1 or -1
   4. It must be equal to 1.

Answer: option C.

26. If any regression coefficient’s value is zero, the two variables are:

1. 1. Independent
   2. Qualitative
   3. Dependent
   4. None of the preceding.

Answer: option A.

27. What is the other term used for dependent variables?

1. 1. Continuous variable
   2. Regression
   3. Regressand
   4. Independent variable
   5. None of the given options.

Answer: option C.

28. Choose the correct option for the regression line passing through the origin.

1. 1. The correlation is zero
   2. The regression coefficient is zero
   3. Intercept is zero
   4. Association is zero.

Answer: option C. 

29. What is the sum of squares of error if all of the actual and estimated values of Y on the regression line are the same?

1. 1. Maximum
   2. Minimum
   3. Zero
   4. Unknown.

Answer: option C.

30. Choose the correct option for two series moving in the opposite directions and the variation in their values being always proportionate.

1. 1. Perfect positive correlation
   2. Negative correlation
   3. Perfect negative correlation
   4. Positive correlation

Answer: option C. 

31. What would be the slopes of two regression lines parallel to each other?

1. 1. Zero
   2. Positive 
   3. Same
   4. Negative

Answer: option C. 

32. For a positive coefficient of determination, the regression equation —–

1. 1. It must have a negative slope
   2. It must have a positive y-intercept
   3. It can either be a positive slope or a negative slope
   4. It must have a positive slope
   5. None of the preceding.

Answer: option C.

33. In a regression analysis, what will be the unit of the dependent variable if the independent variable is measured in kilogrammes?

1. 1. It must be in some unit of weight
   2. It must be in kilogrammes
   3. It can be any unit
   4. It can’t be in kilogrammes.

Answer: option C.

34. Choose the correct option concerning the Null hypothesis.

1. 1. Any wrong decision regarding the Null hypothesis leads to three types of error.
   2. Any wrong decision regarding the Null hypothesis leads to one type of error.
   3. Any wrong decision regarding the Null hypothesis leads to five types of error.
   4. Any wrong decision regarding the Null hypothesis leads to two types of error.

Answer: option D. 

35. For two variables, X and Y, there can be a maximum of

1. 1. Three regression lines
   2. Two regression lines
   3. Four regression lines
   4. One regression line. 

Answer: option B.

36. What is the significance of hypothesis testing?
37. 1. It is a significant assessment of issue
    2. It’s a way of making a powerful statement.
    3. It is a rule for accepting or rejecting the research problem’s hypothesis.
    4. None of the preceding

Answer: option C.