This CorrelationRegression 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 and Regression multiple choice type questions
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?
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
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.
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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:
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.
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.
Sampling Error vs. Sampling Bias
This is a crucial distinction.
Feature
Sampling Error
Sampling Bias (a non-sampling error)
Cause
Random chance
Flawed sampling method
Nature
Unavoidable and measurable
Avoidable and problematic
Effect
Causes imprecision (scatter)
Causes inaccuracy (shift)
Solution
Increase sample size
Fix 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
Clinical Trials are part of clinical research and at the heart of all medical advances. Clinical Trials look at new ways to prevent, detect, or treat diseases under study. Treatments might be new drugs or new combinations of drugs, new surgical procedures or devices, or new ways to use existing treatments.
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Goal of Clinical Trials
The goal of clinical trials is to determine if a new test or treatment works and is safe. Clinical trials can also look at other aspects of care, such as improving the quality of life for people with chronic illness.
Clinical Trials in Clinical Research: Definitions
Clinical Research
Clinical research is a medical research that involves people to test new treatments and therapies.
Clinical Trials
A research study in which one or more human subjects are prospectively assigned to one or more interventions (which may include a placebo or other control) to evaluate the effects of those interventions on health-related biomedical or behavioural outcomes.
Placebo
A placebo is a pill or liquid that looks like the new treatment but does not have any treatment value from active ingredients.
Protocol
A protocol is a carefully designed plan to safeguard the participants’ health and answer specific research questions.
Principal Investigator
A principal investigator is a doctor who leads the clinical research team and, along with the other members of the research team, regularly monitors the study participants’ health to determine the study’s safety and effectiveness.
Healthy Volunteer
A healthy volunteer is a person with no known significant health problems who participates in clinical research to test a new drug, device, or intervention.
Inclusion/ Exclusion Criteria
Inclusion/ exclusion criteria are factors that allow someone to participate in a clinical trial are inclusion criteria. Those that exclude or do not allow participation are exclusion criteria.
Informed Consent
Informed consent explains the risks and potential benefits of a clinical trial before someone decides whether to participate.
Patient Volunteer
A patient volunteer has a known health problem and participates in research to better understand, diagnose, treat, or cure that disease or condition.
Randomization
Randomization is the process by which two or more alternative treatments are assigned to volunteers by chance rather than by choice.
Single or Double Blind Studies
Single or double-blind studies (also called single or double-masked studies) are studies in which the participants do not know which medicine is being used, so they can describe what happens without bias.
Phases of Clinical Trials
Clinical trials are conducted in phases. The trials at each phase have a different purpose and help researchers to answer different questions.
Phase-I Trials: an experimental drug or treatment in a small group of people (20 to 80) for the first time. The purpose is to evaluate its safety and identify side effects.
Phase-II Trials: The experimental drug or treatment is administered to a larger group of people (100 to 300) to determine its effectiveness and to further evaluate its safety.
Phase-III Trials: The experimental drug or treatment is administered to large groups of people (1000 to 3000) to confirm its effectiveness, monitor side effects, and compare it with standard or equivalent treatments.
Phase-IV Trials: After a drug is licensed and approved by the FDA (Food and Drug Administration), researchers track its safety, seeking more information about its risks, benefits, and optimal use.
Types of Clinical Trials
Diagnostic Trials: Determine better tests or procedures for diagnosing a particular disease or condition.
Natural History Studies: Provide valuable information about how disease and health progress.
Prevention Trials: Look for better ways to prevent a disease in people who have never had the disease or to prevent the disease from returning.
Quality of Life Trials (or Supportive Care Trials): Explore and measure ways to improve the comfort and quality of life of people with a chronic illness.
Screening Trials: Test the best way to detect certain diseases or health conditions.
Treatment Trials: Test new treatments, new combinations of drugs, or new approaches to surgery or radiation therapy.
