Correlation and Regression — MCQs
A group of 80 people is being studied to determine the effect of diet modification on cholesterol levels. To compare the mean cholesterol levels before and after the diet modification in this group, which statistical test should be used?
Which finding best predicts poor outcome in acute pancreatitis at admission?
Correlation between height and weight is measured by?
The best method to show the association between height and weight of children in a class is by:
What is the most important criterion in a causal relationship hypothesis?
The relationship between birth rate and maternal hemoglobin is best studied by:
What is the correlation coefficient if regression coefficient of X on Y is 0.8 and Y on X is 0.9?
To understand the relationship between weight and height of a group of school children, the data can graphically be best depicted through
Consider the following statements about correlation between two variables : 1. The correlation is done between an independent variable X and a dependent variable Y. 2. The coefficient of correlation can range from -1 to ∞. 3. If coefficient of correlation (r) is equal to 1, it indicates there is no association between X and Y. 4. Correlation does not necessarily prove causation. Which of the statements given above are correct ?
A researcher has obtained the country-level data on the average Body Mass Index (BMI) and the average sugar intake for 100 countries. Which among the following will be best suited to present the relationship between BMI and sugar intake in the 100 countries?
Correlation and Regression Indian Medical PG Practice Questions and MCQs
Question 1: A group of 80 people is being studied to determine the effect of diet modification on cholesterol levels. To compare the mean cholesterol levels before and after the diet modification in this group, which statistical test should be used?
- A. Paired t-test (Correct Answer)
- B. McNemar test
- C. Chi-square test
- D. Wilcoxon signed-rank test
- E. Independent t-test
Explanation: ***Paired t-test*** - A **paired t-test** is appropriate for comparing means from two related samples, such as "before" and "after" measurements on the **same individuals**. - It assesses whether there is a statistically significant difference between these **dependent observations**. *Independent t-test* - The independent t-test compares means between **two separate groups** (unrelated samples). - It is inappropriate here because we have **paired data** from the same individuals measured twice, not two independent groups. *McNemar test* - The McNemar test is used for comparing **paired nominal data**, typically in a 2×2 table, for example, before-after changes in a proportion or categorical outcome. - It is not suitable for **continuous data** like cholesterol levels. *Chi-square test* - The chi-square test is used to assess the association between **two categorical variables** or to compare observed frequencies with expected frequencies. - It is not designed for comparing means of **continuous variables** in paired samples. *Wilcoxon signed-rank test* - The Wilcoxon signed-rank test is a **non-parametric alternative to the paired t-test**, used when the data are not normally distributed or when the sample size is small. - While it's used for paired data, the paired t-test is generally preferred when parametric assumptions (like **normality**) can be met, especially with a sample size of 80.
Question 2: Which finding best predicts poor outcome in acute pancreatitis at admission?
- A. Ranson score >3 (Correct Answer)
- B. Serum lipase >1000
- C. Blood glucose >200
- D. Pleural effusion
Explanation: ***Ranson score >3*** - A **Ranson score** greater than 3 on admission is a strong predictor of **severe acute pancreatitis** and increased **mortality** [1]. - The Ranson criteria assess multiple parameters, including age, WBC count, LDH, AST, and glucose, providing a comprehensive risk assessment [1]. *Serum lipase >1000* - An elevated **serum lipase level** is highly diagnostic of acute pancreatitis but does not directly correlate with disease severity or prognosis. - While reflecting pancreatic inflammation, lipase levels often do not predict the development of **organ failure** or **necrotizing pancreatitis** [1]. *Blood glucose >200* - **Hyperglycemia** at admission is one of the Ranson criteria, but as a single parameter, it is not as strong a predictor of poor outcome as the complete score. - Isolated high glucose can be due to stress or pre-existing **diabetes**, contributing to some severity but not sufficient for widespread poor prognosis without other factors. *Pleural effusion* - **Pleural effusion** can be a complication of severe pancreatitis, indicating surrounding inflammation. - However, its presence at admission, without other markers of severity, is less predictive of overall poor outcome than a validated scoring system like the Ranson score which assesses multiple systemic factors.
Question 3: Correlation between height and weight is measured by?
- A. Coefficient of variation
- B. Range of variation
- C. Correlation coefficient (Correct Answer)
- D. None of the options
Explanation: ***Correlation coefficient*** - The **correlation coefficient** specifically measures the strength and direction of a **linear relationship** between two variables, such as height and weight. - A positive coefficient indicates that as one variable increases, the other tends to increase, reflecting their interconnectedness. *Coefficient of variation* - The **coefficient of variation (CV)** is a measure of **relative variability** or dispersion, indicating the extent of variability in relation to the mean. - It defines how much dispersion exists in data relative to the mean, but does not describe the relationship between two different variables. *Range of variation* - The **range of variation** simply describes the difference between the **maximum and minimum values** within a single dataset. - It provides information about the spread of a single variable but does not measure any **relationship between two different variables**. *None of the options* - This option is incorrect because the **correlation coefficient** is indeed the appropriate statistical measure for assessing the relationship between height and weight.
Question 4: The best method to show the association between height and weight of children in a class is by:
- A. Line diagram
- B. Scatter diagram (Correct Answer)
- C. Histogram
- D. Bar chart
Explanation: ***Scatter diagram*** - A **scatter plot** is the most appropriate method to visualize the relationship or **association** between two continuous variables, such as height and weight. - Each point on the graph represents a child's height (x-axis) and weight (y-axis), allowing for the observation of **trends** and **correlation**. *Bar chart* - Bar charts are predominantly used for comparing **categorical data** or discrete values, not for showing the relationship between two continuous variables. - They display the frequency or value of different categories, which is not suitable for visualizing a **correlation** between height and weight. *Line diagram* - Line diagrams are primarily used to show **trends over time** or sequences, where data points are connected by lines. - They are not ideal for illustrating the association between two independent continuous variables at a single point in time. *Histogram* - A histogram is used to represent the **distribution of a single continuous variable**, showing its frequency within defined ranges or "bins." - It does not allow for the display or analysis of the **relationship between two different variables** simultaneously.
Question 5: What is the most important criterion in a causal relationship hypothesis?
- A. Temporal association (Correct Answer)
- B. Coherence of association
- C. Specificity of association
- D. Strength of association
Explanation: ***Temporal association*** - This is the **sine qua non** of causality, meaning the exposure or cause must always precede the outcome or effect in time. - Without the exposure occurring before the disease, a causal link cannot be established, even if other criteria are met. *Coherence of association* - This refers to the consistency of findings with current scientific knowledge and **biological plausibility**. - While important for supporting causality, a coherent explanation is not sufficient in itself to prove causation and may even be misleading if current knowledge is incomplete. *Specificity of association* - This criterion suggests that a single exposure should lead to a single outcome, or a single outcome should be caused by a single exposure. - However, many diseases have **multiple causes**, and many exposures can lead to multiple effects, making this a weak criterion in modern epidemiology. *Strength of association* - A **strong association**, often measured by a high relative risk or odds ratio, makes a causal relationship more likely but does not guarantee it. - Strong associations can still be due to **confounding factors** or bias, and weak associations can be causal.
Question 6: The relationship between birth rate and maternal hemoglobin is best studied by:
- A. Sensitivity and specificity.
- B. Correlation and regression. (Correct Answer)
- C. Standard error of difference between two means.
- D. Standard error of difference between two proportions.
Explanation: ***Correlation and regression.*** - **Correlation** measures the strength and direction of a linear relationship between two quantitative variables (birth rate and maternal hemoglobin levels). - **Regression analysis** allows for modeling the relationship between variables, enabling prediction of birth rate based on maternal hemoglobin, or vice versa, and quantifying the effect of one on the other. *Sensitivity and specificity.* - These concepts are used to evaluate the performance of a **diagnostic test** or screening tool in correctly identifying individuals with and without a specific condition. - They are not appropriate for studying the relationship between two continuous variables like birth rate and maternal hemoglobin. *Standard error of difference between two means.* - This statistical measure is used to determine if there is a **statistically significant difference** between the means of two independent groups, typically when comparing a quantitative outcome between these groups. - It is not suitable for assessing the continuous relationship or association between two continuous variables. *Standard error of difference between two proportions.* - This measure is employed to assess whether there is a **statistically significant difference** between the proportions or percentages of an outcome in two different groups. - It is used for categorical data and is not applicable for analyzing the relationship between two continuous variables.
Question 7: What is the correlation coefficient if regression coefficient of X on Y is 0.8 and Y on X is 0.9?
- A. 0.95
- B. 0.85 (Correct Answer)
- C. 0.81
- D. 0.72
Explanation: ***Correct: 0.85*** - The correlation coefficient (r) is the **geometric mean** of the two regression coefficients - Formula: r = √(b_xy × b_yx), where b_xy is the regression coefficient of X on Y and b_yx is the regression coefficient of Y on X - Calculation: r = √(0.8 × 0.9) = √0.72 ≈ **0.8485**, which rounds to **0.85** - Since both regression coefficients are positive, the correlation is positive *Incorrect: 0.95* - This would be obtained by taking the **arithmetic mean** [(0.8 + 0.9)/2 = 0.85... wait, that's not 0.95] - Actually, this value is too high and doesn't result from any standard calculation with these regression coefficients - The correct method requires the **geometric mean** (square root of the product), not any simple average *Incorrect: 0.81* - This appears to be the square of one regression coefficient (0.9² = 0.81) - However, the correlation coefficient requires the **square root of the product** of both coefficients, not squaring a single coefficient - This is a common error in calculation *Incorrect: 0.72* - This is the **product** of the two regression coefficients (0.8 × 0.9 = 0.72) - This is an intermediate step in the calculation, but not the final answer - The correlation coefficient requires taking the **square root** of this product: √0.72 ≈ 0.85
Question 8: To understand the relationship between weight and height of a group of school children, the data can graphically be best depicted through
- A. Histogram
- B. Scatter diagram (Correct Answer)
- C. Bar diagram
- D. Pictogram
Explanation: ***Scatter diagram*** - A **scatter diagram** (also called a scatter plot) is ideal for showing the relationship between **two continuous variables**, such as weight and height. - Each point on the graph represents an individual's paired values for weight and height, allowing visual identification of **patterns or correlations**. *Histogram* - A **histogram** is used to display the distribution of **a single continuous variable**, showing the frequency of data points within specific intervals or bins. - It would not effectively demonstrate the **relationship or correlation** between two variables simultaneously. *Bar diagram* - A **bar diagram** (or bar chart) is typically used for comparing **categorical data** or discrete values, showing frequencies or proportions for different categories. - It is not suitable for visualizing the relationship between **two continuous numerical variables** like weight and height. *Pictogram* - A **pictogram** uses images or symbols to represent data, often used for presenting simple statistics to a general audience. - It is generally used for **categorical data** or simple comparisons and lacks the precision needed to display the continuous relationship between weight and height.
Question 9: Consider the following statements about correlation between two variables : 1. The correlation is done between an independent variable X and a dependent variable Y. 2. The coefficient of correlation can range from -1 to ∞. 3. If coefficient of correlation (r) is equal to 1, it indicates there is no association between X and Y. 4. Correlation does not necessarily prove causation. Which of the statements given above are correct ?
- A. 1 only
- B. 4 only (Correct Answer)
- C. 1, 2 and 3
- D. 1 and 4 only
Explanation: ***Correct: 4 only*** - **Correlation** measures the strength and direction of a linear relationship between two variables, but it **does not imply that one causes the other**; other factors or confounding variables might be involved. - This statement is a fundamental principle in statistics, emphasizing that causality requires more rigorous evidence, such as controlled experiments, beyond a simple correlation. - **Only statement 4 is correct** among all the given statements. *Incorrect: 1 only* - While correlation is often explored between dependent and independent variables, it can also be used to assess the relationship between **any two quantitative variables**, whether one is clearly designated as independent or dependent. - Statement 1 is partially incorrect as correlation isn't exclusively between designated independent and dependent variables. *Incorrect: 1, 2 and 3* - Statement 1 is partially incorrect as correlation isn't exclusively between designated independent and dependent variables. - Statement 2 is incorrect because the **coefficient of correlation (r) ranges from -1 to +1**, not to infinity, with -1 indicating a perfect negative correlation and +1 a perfect positive correlation. - Statement 3 is incorrect because an **r equal to 1 indicates a perfect positive linear association** between X and Y, meaning they move in the same direction proportionally, not no association. *Incorrect: 1 and 4 only* - Statement 1 is incorrect because **correlation can be performed between any two variables** to assess their relationship, not just an explicitly independent and dependent pair. - While statement 4 is correct, the inclusion of statement 1 makes this option incorrect.
Question 10: A researcher has obtained the country-level data on the average Body Mass Index (BMI) and the average sugar intake for 100 countries. Which among the following will be best suited to present the relationship between BMI and sugar intake in the 100 countries?
- A. Frequency polygon
- B. Bar chart
- C. Scatter diagram (Correct Answer)
- D. Pie diagram
Explanation: ***Scatter diagram*** - A **scatter diagram** is ideally suited for visualizing the relationship or **correlation** between two continuous variables, in this case, average BMI and average sugar intake per country. - Each point on the diagram represents a single country, with its coordinates determined by its corresponding BMI and sugar intake values, allowing for easy identification of patterns or trends. *Frequency polygon* - A **frequency polygon** is used to display the **frequency distribution** of a single continuous variable, showing the shape of the data. - It is not designed to show the relationship between two different variables. *Bar chart* - A **bar chart** is typically used to compare **categorical data** or show changes in a **single variable over time**. - It does not effectively display the relationship or correlation between two continuous variables like BMI and sugar intake. *Pie diagram* - A **pie diagram** is used to represent **proportions** or percentages of a whole for a single categorical variable. - It is not suitable for visualizing the relationship between two continuous quantitative variables.
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