Important MCQs on Correlation and Regression 3

The post is about MCQs on Correlation and Regression Analysis with Answers. There are 20 multiple-choice questions covering the topics related to correlation and regression analysis, interpretation of correlation and regression coefficients, relationship between variables, and correlation and regression coefficients. Let us start with MCQs on Correlation and Regression.

MCQs about Correlation and Regression Analysis

1. A perfect negative correlation is signified by

 
 
 
 

2. The coefficient of Correlation values lies between

 
 
 
 

3. If $\hat{Y}=a$ then $r_{xy}$?

 
 
 
 

4. In Correlation, both variables are always

 
 
 
 

5. If $X$ and $Y$ are independent of each other, the Coefficient of Correlation is

 
 
 
 

6. If $r=0.6, b_{yx}=1.2$ then $b_{xy}=?$

 
 
 
 

7. The Coefficient of Correlation $r$ is independent of

 
 
 
 

8. When $b_{xy}$ is positive, then $b_{yx}$ will be

 
 
 
 

9. When two regression coefficients bear the same algebraic signs, then the correlation coefficient will be

 
 
 
 

10. If $r_{xy} = -0.84$ then $r_{yx}=?$

 
 
 
 

11. If two variables oppose each other then the correlation will be

 
 
 
 

12. When the regression line passes through the origin then

 
 
 
 

13. If $b_{yx} <0$ and $b_{xy} =<0$, then $r$ is

 
 
 
 

14. In the regression line $Y=a+bX$

 
 
 
 

15. The Coefficient of Correlation between $X$ and $X$ is

 
 
 
 

16. In the regression line $Y=a+bX$ the following is always true

 
 
 
 

17. Two regression lines are parallel to each other if their slope is

 
 
 
 

18. The regression coefficient is independent of

 
 
 
 

19. It is possible that two regression coefficients have

 
 
 
 

20. The Coefficient of Correlation between $U=X$ and $V=-X$ is

 
 
 
 

MCQs on Correlation and Regression with Answers

MCQs on Correlation and Regression Quiz with Answers
  • The coefficient of Correlation values lies between
  • If $r_{xy} = -0.84$ then $r_{yx}=?$
  • In Correlation, both variables are always
  • If two variables oppose each other then the correlation will be
  • A perfect negative correlation is signified by
  • The Coefficient of Correlation between $U=X$ and $V=-X$ is
  • The Coefficient of Correlation between $X$ and $X$ is
  • The Coefficient of Correlation $r$ is independent of
  • If $X$ and $Y$ are independent of each other, the Coefficient of Correlation is
  • If $b_{yx} <0$ and $b_{xy} =<0$, then $r$ is
  • If $r=0.6, b_{yx}=1.2$ then $b_{xy}=?$
  • When the regression line passes through the origin then
  • Two regression lines are parallel to each other if their slope is
  • When $b_{xy}$ is positive, then $b_{yx}$ will be
  • If $\hat{Y}=a$ then $r_{xy}$?
  • When two regression coefficients bear the same algebraic signs, then the correlation coefficient will be
  • It is possible that two regression coefficients have
  • The regression coefficient is independent of
  • In the regression line $Y=a+bX$
  • In the regression line $Y=a+bX$ the following is always true
Statistics MCQs on Correlation and Regression

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Best Correlation and Regression Quiz 2

The post is about the Correlation and Regression Quiz. There are 20 multiple-choice questions. The quiz covers the topics related to correlation analysis and regression analysis, Basic concepts, assumptions, and violations of correlation and regression analysis, Model selection criteria, interpretation of correlation and regression coefficients, etc.

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Online Correlation and Regression Quiz with Answers

Correlation and Regression Quiz with Answers
  • The strength (degree) of the correlation between a set of independent variables $X$ and a dependent variable $Y$ is measured by
  • The percent of the total variation of the dependent variable $Y$ explained by the set of independent variables $X$ is measured by
  • A coefficient of correlation is computed to be -0.95 means that
  • Let the coefficient of determination computed to be 0.39 in a problem involving one independent variable and one dependent variable. This result means that
  • The relationship between the correlation coefficient and the coefficient of determination is that
  • Multicollinearity exists when
  • If “time” is used as the independent variable in a simple linear regression analysis, then which of the following assumptions could be violated
  • In multiple regression, when the global test of significance is rejected, we can conclude that
  • A residual is defined as
  • What test statistic is used for a global test of significance?
  • If the value of any regression coefficient is zero, then two variables are said to be
  • In the straight line graph of the linear equation $Y=a+bX$, the slope will be upward if
  • In the straight line graph of the linear equation $Y=a+bX$, the slope will be downward if
  • In the straight line graph of the linear equation $Y=a+BX$, the slope is horizontal if
  • For the regression $\hat{Y}=5$, the value of regression coefficient of $Y$ on $X$ will be
  • If $\beta_{yx} = -1.36$ and $\beta_{xy} = -0.34$ then $r_{xy} =$
  • If one regression coefficient is greater than one then the other will be
  • To determine the height of a person when his weight is given is
  • The dependent variable is also called
  • The dependent variable is also called
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Best Correlation and Regression MCQs 1

The post is about Correlation and Regression MCQs. There are 20 multiple-choice questions. The quiz covers topics related to the basics of correlation Analysis and regression analysis, correlation and regression coefficients, graphical representation relationships between variables, simple linear regression models and multiple linear regression models, and assumptions related to correlation and regression models. Let us start with the Correlation and Regression MCQs Quiz.

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Online Correlation and Regression MCQs

Online Correlation and Regression MCQs with Answers
  • The estimate of $\beta$ in the regression equation $Y=\alpha+\beta\,X + e$ by the method of least square is:
  • If $\beta_{XY}$ and $\beta_{YX}$ are two regression coefficients, they have
  • The average of two regression coefficients is always greater than or equal to the correction coefficient is called:
  • If $\beta_{YX}>1$, then $\beta_{XY}$ is:
  • If the two lines of regression are perpendicular to each other, the correlation coefficient $r=$ is:
  • The regression coefficient is independent of
  • If each of $X$ variable is divided by 5 and $Y$ by 10 then $\beta_{YX}$ by coded value is:
  • The geometric mean of the two regression coefficient $\beta_{YX}$ and $\beta_{XY}$ is equal to:
  • If $X$ and $Y$ are two independent variates with variance $\sigma_X^2$ and $\sigma_Y^2$, respectively, the coefficient of correlation between $X$ and ($X-Y$) is equal to:
  • In multiple linear regression analysis, the square root of Mean Squared Error (MSE) is called the:
  • The range of a partial correlation coefficient is:
  • Homogeneity of three or more population correlation coefficients can be tested by
  • If $\rho$ is the correlation coefficient, the quantity $\sqrt{1-\rho^2}$ is termed as
  • If the correlation coefficient between the variables $X$ and $Y$ is $\rho$, the correlation coefficient between $X^2$ and $Y^2$ is
  • The lines of regression intersect at the point
  • If $\rho=0$, the lines of regression are:
  • An investigator reports that the arithmetic mean of two regression coefficients of a regression line is 0.7 and the correlation coefficient is 0.75. Are the results
  • If regression line $\hat{y}=5$ then value of regression coefficient of $y$ on $x$ is
  • When two variables move in the same direction then the correlation between the variables is
  • If all the actual and estimated values of $Y$ are the same on the regression line, the sum of squares of errors will be
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Akaike Information Criteria: A Comprehensive Guide

The Akaike Information Criteria/Criterion (AIC) is a method used in statistics and machine learning to compare the relative quality of different models for a given dataset. The AIC method helps in selecting the best model out of a bunch by penalizing models that are overly complex. Akaike Information Criterion provides a means for comparing among models i.e. a tool for model selection.

  • A too-simple model leads to a large approximation error.
  • A too-complex model leads to a large estimation error.

AIC is a measure of goodness of fit of a statistical model developed by Hirotsugo Akaike under the name of “an information Criteria (AIC) and published by him in 1974 first time. It is grounded in the concept of information entropy in between bias and variance in model construction or between accuracy and complexity of the model.

The Formula of Akaike Information Criteria

Given a data set, several candidate models can be ranked according to their AIC values. From AIC values one may infer that the top two models are roughly in a tie and the rest far worse.

$$AIC = 2k-ln(L)$$

where $k$ is the number of parameters in the model, and $L$ is the maximized value of the likelihood function for the estimated model.

Akaike Information Criteria/ Criterion (AIC)

For a set of candidate models for the data, the preferred model is the one that has a minimum AIC value. AIC estimates relative support for a model, which means that AIC scores by themselves are not very meaningful

Akaike Information Criteria focuses on:

  • Balances fit and complexity: A model that perfectly fits the data might not be the best because it might be memorizing the data instead of capturing the underlying trend. AIC considers both how well a model fits the data (goodness of fit) and how complex it is (number of variables).
  • A lower score is better: Models having lower AIC scores are preferred as they achieve a good balance between fitting the data and avoiding overfitting.
  • Comparison tool: AIC scores are most meaningful when comparing models for the same dataset. The model with the lowest AIC score is considered the best relative to the other models being evaluated.

Summary

The AIC score is a single number and is used as model selection criteria. One cannot interpret the AIC score in isolation. However, one can compare the AIC scores of different model fits to the same data. The model with the lowest AIC is generally considered the best choice.

The AIC is the most useful model selection criterion when there are multiple candidate models to choose from. It works well for larger datasets. However, for smaller datasets, the corrected AIC should be preferred. AIC is not perfect, and there can be situations where it fails to choose the optimal model.

There are many other model selection criteria. For more detail read the article: Model Selection Criteria

Akaike Information Criteria

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