Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

Regression Correlation MCQs 14

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Master the fundamentals of statistical relationships with this comprehensive 20-question Multiple Choice Quiz on Regression Correlation MCQs. Designed for students, researchers, data analysts, and aspiring data scientists, this quiz tests your understanding of key concepts essential for exams and job interviews. Challenge yourself with problems on finding regression equations, correlation coefficients, means, standard deviations, covariance, and the coefficient of determination. Perfect your skills in interpreting data and predicting values to solidify your grasp on these critical statistical techniques. Let us start with the Regression Correlation MCQs now.

Online Regression Correlation MCQs with Answers

Online MCQs about Correlation and Regression Analysis

1. The average price of an item is Rs. 25.5 with a standard deviation of Rs. 2.4 and the average demand of that item is 40 units per day with a standard deviation of 6 units. Correlation between them is $-0.8$. When the price is Rs. 24, then the estimated demand of that item is?

 
 
 
 

2. The two regression equations are given as: $3X+2Y=26$ and $6X+Y=31$. What are the mean values of $X$ and $Y$?

 
 
 
 

3. The value of $a_{xy}$ in the regression equation $2X+3Y+50=0$ is

 
 
 
 

4. For the two variables, the regression of $Y$ on $X$ is $4X-5Y-90=0$ and the regression equation of $X$ on $Y$ is $X+kY-6=0$. If the coefficient of determination is 0.48, then the value of $k$ is

 
 
 
 

5. The regression equations of two variables $X$ and $Y$ are given $3X+2Y-26=0$ and $6X+Y-31=0$. What is the value of the correlation coefficient?

 
 
 
 

6. Given that $b_{yx}=1.36$ and $b_{xy}=0.613$ then the coefficient of determination is

 
 
 
 

7. Two given regression equations are $2X+3Y=5$ and $x+2Y=4$, then equation of the $Y$ on $X$ is

 
 
 
 

8. The correlation coefficient between two variables $X$ and $Y$ is 0.8, and their covariance is 20. Also standard deviation of $X$ is 4; what is the standard deviation of $Y$?

 
 
 
 

9. The statement “two regression lines always intersect at the mean value of $X$ and $Y$” is

 
 
 
 

10. The given data $\overline{x} = 36$, $\overline{y}=85$, $\sigma=8$, $\sigma_x=11$, $r=0.6$ then find the value of $X$ if $Y=75$.

 
 
 
 

11. The regression coefficients are equal to zero if $r$ is equal to

 
 
 
 

12. The covariance between variables $X$ and $Y$ of five items is 6, and their standard deviations are 2.45 and 2.6, respectively. What is the value of $r$?

 
 
 
 

13. If $r=0.6$, then the coefficient of non-determination is

 
 
 
 

14. The correlation coefficient is a

 
 
 
 

15. The angle between the two regression lines depends upon

 
 
 
 

16. For 10 observations on Price ($X$) and Supply ($Y$), the following data obtained: $\Sigma X = 130, \Sigma Y=220, \Sigma X^2 = 2288, \Sigma Y^2=5506, $\Sigma XY=3467$. Estimate the value of the supply if the price is 16?

 
 
 
 

17. Given the following data $\Sigma Y=294$, $\Sigma X = 490$, $\Sigma XY=3125$, $\Sigma X^2 = 5350$, $\Sigma Y^2 = 1964$ and $n=49$, then what is the value of correlation coefficient?

 
 
 
 

18. The slope of the regression line of $Y$ on $X$ is equal to

 
 
 
 

19. Given that $r=0.8$, $\Sigma XY = 60$, $\delta_Y = 2.5$, $\Sigma X^2=90$, where $X$ and $Y$ are the deviations from their respective means, then the value of $n$ is

 
 
 
 

20. The value of $b_{yx}$ in the regression equation $2X + 3Y +50 =0$ is

 
 
 
 

Online Regression Correlation MCQs with Answers

  • For the two variables, the regression of $Y$ on $X$ is $4X-5Y-90=0$ and the regression equation of $X$ on $Y$ is $X+kY-6=0$. If the coefficient of determination is 0.48, then the value of $k$ is
  • The two regression equations are given as: $3X+2Y=26$ and $6X+Y=31$. What are the mean values of $X$ and $Y$?
  • Two given regression equations are $2X+3Y=5$ and $x+2Y=4$, then equation of the $Y$ on $X$ is
  • The average price of an item is Rs. 25.5 with a standard deviation of Rs. 2.4 and the average demand of that item is 40 units per day with a standard deviation of 6 units. Correlation between them is $-0.8$. When the price is Rs. 24, then the estimated demand of that item is?
  • Given the following data $\Sigma Y=294$, $\Sigma X = 490$, $\Sigma XY=3125$, $\Sigma X^2 = 5350$, $\Sigma Y^2 = 1964$ and $n=49$, then what is the value of correlation coefficient?
  • The correlation coefficient between two variables $X$ and $Y$ is 0.8, and their covariance is 20. Also standard deviation of $X$ is 4; what is the standard deviation of $Y$?
  • The covariance between variables $X$ and $Y$ of five items is 6, and their standard deviations are 2.45 and 2.6, respectively. What is the value of $r$?
  • Given that $r=0.8$, $\Sigma XY = 60$, $\delta_Y = 2.5$, $\Sigma X^2=90$, where $X$ and $Y$ are the deviations from their respective means, then the value of $n$ is
  • If $r=0.6$, then the coefficient of non-determination is
  • The statement “two regression lines always intersect at the mean value of $X$ and $Y$” is
  • The value of $b_{yx}$ in the regression equation $2X + 3Y +50 =0$ is
  • The value of $a_{xy}$ in the regression equation $2X+3Y+50=0$ is
  • The regression coefficients are equal to zero if $r$ is equal to
  • The angle between the two regression lines depends upon
  • The slope of the regression line of $Y$ on $X$ is equal to
  • Given that $b_{yx}=1.36$ and $b_{xy}=0.613$ then the coefficient of determination is
  • The regression equations of two variables $X$ and $Y$ are given $3X+2Y-26=0$ and $6X+Y-31=0$. What is the value of the correlation coefficient?
  • The given data $\overline{x} = 36$, $\overline{y}=85$, $\sigma=8$, $\sigma_x=11$, $r=0.6$ then find the value of $X$ if $Y=75$.
  • For 10 observations on Price ($X$) and Supply ($Y$), the following data obtained: $\Sigma X = 130, \Sigma Y=220, \Sigma X^2 = 2288, \Sigma Y^2=5506, $\Sigma XY=3467$. Estimate the value of the supply if the price is 16?
  • The correlation coefficient is a

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Correlation Regression Quiz 13

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This Correlation Regression Quiz features essential MCQs on regression lines, coefficients, and interpretation. Prepare for your statistics exam or data analyst job test with this comprehensive correlation and regression quiz. Includes 20 MCQs on the coefficient of determination $(r^2$), regression coefficients, scatter plots, and the method introduced by Francis Galton. Ideal for students and aspiring data scientists. Let us start with the Online Correlation Regression Quiz now.

Online Correlation Regression Quiz with Answers
Please go to Correlation Regression Quiz 13 to view the test

Online Correlation Regression Quiz 13 with Answers

  • What is the necessary condition for the value of the regression coefficients?
  • Which of the following is the G.M. of two regression coefficients?
  • If $r$ is negative, then which of the following is true?
  • If the coefficient of correlation between two variables is 0.7, then the percentage of the variation uncounted for is
  • If the coefficient of correlation between two variables is $-0.9$, then the coefficient of determination is
  • The regression coefficients remain unchanged due to
  • If the value of $r=0$, then which of the following must be true?
  • What is the type of correlation between temperature and sales of cold drinks in summer?
  • The correlation coefficient shows the
  • If the change of one variable and the change of the other variable are constant (equal change), then the correlation is
  • The values of the coefficient of determination always lie in
  • The regression line, also known as
  • A numerical measure which shows a possible change in the value of $X$ for a unit in $Y$ is denoted as
  • In the regression line $Y=a + bX$, the value of $a$ is known as
  • What is the value of $b$ known as, in $Y=a+bX$ is
  • If the slopes of two regression lines are equal, then
  • What is the intersection point (common point) of two regression lines?
  • For a perfect strong correlation, if $b_{yx}=-0.5$, then what is the value of$b_{xy}$?
  • The term “regression was initially introduced by
  • If the regression equation of $Y$ on $X$ is $9X+nY+8=0$ and the equation of $X$ on $Y$ is $2X+Y-m=0$ and the mean of $X$ and $Y$ is $-1$ and $4$, respectively, then the values of $m$ and $n$ are

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Size of Sampling Error

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In this post, we will discuss sampling error and the size of sampling error. Sampling error is the difference between a sample statistic (such as a sample mean) and the true population parameter (the actual population mean). Sampling error arises because a sample is being studied instead of the entire population.

The word “error” in sampling error may be misleading for someone. It does not mean that you made a mistake in your research process. Sampling error is a statistical concept that exists even when your sampling is perfectly random and your execution is flawless.

Cause of Sampling Error

Sampling error is caused by random chance. When someone randomly selects a subset of a population, that specific subset will never have the exact same characteristics as the entire population. This chance variation is sampling error. For example

Suppose you have a large bowl of soup (consider it the population), and you taste a single spoonful (it is a sample). The flavour of that spoonful will probably be very close to the whole bowl, but it might be a tiny bit saltier or have one more piece of vegetable than the average spoonful. This small natural difference is the “Sampling Error”. It is not a mistake that you made; it is an inevitable result of sampling.

How is it measured?

Let $\hat{\theta}$ be a sample statistic and let $\theta$ be its true population parameter, then sampling error is
$$Sampling\,\, Error = \hat{\theta} – \theta$$

For example, $\overline{x}$ be the sample mean and $\mu$ is the true population parameter then

$$Sampling\,\, Error = \overline{x} – \mu$$

The most common way to quantify Sampling Error is the computation of standard error (SE). The computation of the standard error of the mean (SEM) estimates how much the sample average is likely to vary from the true population mean. A smaller standard error means less variability and more precision in the estimate.

The standard error formula is

$$SE = \frac{s}{\sqrt{n}}$$

where $s$ is the sample standard deviation and $n$ is the sample size.

Factors Affecting the Size of Sampling Error

Two main factors control the size of sampling error:

  1. Sample Size (n): This is the most important factor.
    • Larger Sample Size → Smaller Sampling Error. As the sample size increases, the sample becomes a better and better representation of the population. That is, the sampling error shrinks.
    • This is why national polls survey thousands of people, not just a few dozen.
  2. Population Variability (Standard Deviation s):
    • More Variable Population → Larger Sampling Error. If the individuals in the population are very diverse (e.g., “ages of all people in a country”), any given sample might be less representative. If the population is very homogeneous (e.g., “diameters of ball bearings from the same machine”), a small sample will be very accurate.

This relationship is captured in the formula for the Standard Error above.

Size of Sampling Error

Sampling Error vs. Sampling Bias

This is a crucial distinction.

FeatureSampling ErrorSampling Bias (a non-sampling error)
CauseRandom chanceFlawed sampling method
NatureUnavoidable and measurableAvoidable and problematic
EffectCauses imprecision (scatter)Causes inaccuracy (shift)
SolutionIncrease sample sizeFix the sampling 333method
  • Sampling Error: Firing a rifle multiple times at a target. The shots will cluster tightly (small error) or be spread out (large error) around the bullseye.
  • Sampling Bias: The rifle’s scope is miscalibrated. All your shots are consistently off-target in one direction, missing the true bullseye.

Sampling Error: Real World Example

Suppose you want to know the average height of all 10000 students at the university (the population). The average height is 5’8″ (the parameter is known to you). You take a random sample of 100 students and calculate their average height. It comes out to 5’7.5″. You take another random sample of 100 different students, the average for this sample is 5’8.5″.

The difference between your first sample’s results (5’7.5″) and the true value (5’8″) is -0.5inches. This is the sampling error for that first sample. The difference for the second sample is +0.5 inches. This is the sampling error for the second sample.

This variation is natural and expected. Similarly, if the sample size is increased to 500 students, the sample averages (e.g., 5’7.9″, 5’8.1″) would likely be much closer to the true 5’8″, meaning that the sampling error would be smaller.

Sampling Error: Summary

  • What it is: Natural variation between a sample and the population.
  • What it’s not: A mistake or bias in the research design.
  • Why it matters: It tells us the precision of our sample-based estimates.
  • How to reduce it: Increase the sample size.
  • How to measure it: Calculate the Standard Error (SE).

FAQs about Sampling Error and Size of Sampling Error

  • What is sampling error?
  • What is meant by the size of sampling error?
  • How can sampling error be reduced?
  • Give some real-world examples related to sampling error.
  • How is sampling error computed?
  • Describe the causes of sampling error.
  • What is the difference between error, sampling error, and sampling bias

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