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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Can ‘r’ lie outside -1 and 1 range depending on the type of data? |
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Answer» For any type of data, correlation (r) cannot lie outside the -1 and +1 range. The minimum limit of ‘r’ is -1 and +1 range. The minimum limit of ‘r’ is -1 and the maximum limit of r is +1. As a result, r can never lie outside these two limits. Symbolically. -1 ≤ r ≥ 1 If in any exercise, ‘r’ is outside this range it indicates error in calculation. |
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| 2. |
The range of simple correlation coefficient is : |
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Answer» 1. 0 to infinity 2. Minus one to plus one 3. Minus infinity to infinity |
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| 3. |
Why is ‘r’ preferred to co-variance as a measure of association? |
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Answer» ‘r ’ is Perferred to co-variance as a measure of association because it studies and Measures the direction and intensity of relationship among variables. It is due to the following reasons: 1. The correlation co – efficient (r) has no unit. 2. The correlation co – efficient is independent of origin as well as a scale |
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| 4. |
Can simple correlation co – efficient measure any type of relationship? |
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Answer» Simple correlation co-efficient cannot measure any type of relationship. It measures any type of relationship only between two variables. If the variables are more than two or we want to measure the correlation between the productivity of wheat, temperature, and quantity of rain, then simple correlation cannot measure this type of relationship. This type of relationship can be measured with the help of partial or multiple correlation co – efficient. |
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| 5. |
If `r_(xy)` = 0 , the varaible X and Y are :A. Linearly relatedB. Not linearly relatedC. independent |
| Answer» Correct Answer - C | |
| 6. |
If precisely measured data are available, the simple correlation coefficient is: |
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Answer» 1. More-accurate than rank correlation coefficient. 2. Less accurate than rank correlation coefficient. 3. As accurate as the rank correlation coefficient. |
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| 7. |
Why does rank correlation co-efficient differ from Pearsonian correlation coefficient? |
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Answer» Rank correlation co-efficient is more often used to measure the linear relationship between the qualitative variable whereas Karl Pearson’s method of correlation co – efficient measures the linear relationship between the quantitative variables. |
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| 8. |
Interpret the values of r as 1, -1, and 0. |
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Answer» 1. r as 1 means that there is perfect positive relationship between two variables. 2. r as -1 means that there is perfect negative relationship between two variables. 3. r as 0 means that there is lack of correlation between two variables. |
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| 9. |
Does zero correlation does not mean independence? |
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Answer» No, zero correlation does not mean independence. If there is zero correlation, it means the two variables are not correlated and there is no linear relation between them. However, other types of relation may be there and they may be not independent. |
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| 10. |
When is rank correlation more precise than simple correlation coefficient? |
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Answer» Rank correlation is more precise than simple correlation when the variables cannot be measured meaningfully as in the case of prices, income, weight etc. Ranking may be more meaningful when the measurement of the variables are suspect. Ranking may be a better alternative to quantification of qualities. |
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| 11. |
The range of simple correlation cofficient is :A. 0 to infinityB. minus one to plus oneC. minus infinity to infinity |
| Answer» Correct Answer - B | |
| 12. |
The variable which influences the values or is used for prediction is called:(a) Dependent variable (b) Independent variable (c) Explained variable (d) Regressed |
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Answer» (b) Independent variable |
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| 13. |
If r = 0, the variable X and Y are |
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Answer» 1. Linearly related 2. Not linearly related 3. Independent |
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| 14. |
I f precisely measured data are available the simple correlation cofficient is :A. more accurate than rank correlation cofficientB. less accurate than rank correlation cofficientC. as accurate as the rank correlation cofficient |
| Answer» Correct Answer - C | |
| 15. |
The unit of correlation between height in feet and weight in kg is:A. kg/feetB. percentageC. non-existent |
| Answer» Correct Answer - C | |
| 16. |
When x falls, y also falls. There is perfect correlation between the two. The correlation coefficient between the two isA. ZeroB. InfinityC. `+1`D. `-1` |
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Answer» Correct Answer - C C |
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| 17. |
Define correlation . Give its importance in statistics . |
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Answer» When the relationship is of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in a brief formula is known as correlation. Following observations highlight the importance or significance of correlation as a statistical method: 1) Formation of laws and concepts: The study of correlation shows the direction and degree of relationship between the variables. This has helped the formation of various laws and concepts in economic theory, such as law of demand and concept of elasticity of demand. 2) Cause and Effect relationship: Correlation coefficient sometimes suggests cause and effect relationship between different variables. This helps in understanding why certain variables behave the way they behave. 3) Business decisions: Correlation analysis facilitates business decisions because the trend path of one variable may suggest the expected changes in the other. Accordingly, the businessman may plan his business decisions for the future. 4) Policy Formulation: Correlation analysis also helps policy formulation. If the government finds a negative correlation between tax and tax collection, it should pursue the policy of low tax rate. Because, low tax rate would lead to high tax collection. |
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| 18. |
Describe the various degrees of correlation . |
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Answer» Correlation exists in various degrees: 1.Perfect positive correlation: If an increase in the value of one variable is followed by the same proportion of increase in other related variable or if a decrease in the value of one variable is followed by the same proportion of decrease in other related variable, it is perfect positive correlation. eg: if 10% rise in price of a commodity results in 10% rise in its supply, the correlation is perfectly positive. Similarly, if 5% full in price results in 5% fall in supply, the correlation is perfectly positive. 2.Perfect Negative correlation: If an increase in the value of one variable is followed by the same proportion of decrease in other related variable or if a decrease in the value of one variable is followed by the same proportion of increase in other related variably it is Perfect Negative Correlation. For example if 10% rise in price results in 10% fall in its demand the correlation is perfectly negative. Similarly if 5% fall in price results in 5% increase in demand, the correlation is perfectly negative. 3.Limited Degree of Positive correlation: When an increase in the value of one variable is followed by a non-proportional increase in other related variable, or when a decrease in the value of one variable is followed by a non-proportional decrease in other related variable, it is called limited degree of positive correlation. For example, if 10% rise in price of a commodity results in 5% rise in its supply, it is limited degree of positive correlation. Similarly if 10% fall in price of a commodity results in 5% fall in its supply, it is limited degree of positive correlation. 4.Limited degree of Negative correlation: When an increase in the value of one variable is followed by a non-proportional decrease in other related variable, or when a decrease in the value of one variable is followed by a non-proportional increase in other related variable, it is called limited degree of negative correlation. For example, if 10% rise in price results in 5% fall in its demand, it is limited degree of negative correlation. Similarly, if 5% fall in price results in 10% increase in demand, it is limited degree of negative correlation. 5.Zero Correlation (Zero Degree correlation): If there is no correlation between variables it is called zero correlation. In other words, if the values of one variable cannot be associated with the values of the other variable, it is zero correlation. |
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| 19. |
Explain the concept of correlation .what is the basic difference between :(i) Linear and non- linear correlation, and (ii) positive and negative correlation . |
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Answer» The statistical technique that studies the degree of relationships is called technique of correlation. For example, increase in level of employment results in increase in output. I) When two variable changes in a constant proportion, it is called a linear correlation, whereas, When the two variables do not change in any constant proportion, the relationship is said to be non-linear. II) Correlation is perfectly positive when proportional change in two variables is in the same direction. Whereas, correlation is perfectly negative when proportional change in two variables is in the opposite direction. |
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| 20. |
If `r=0.997,sumxy=46,bar(X)=4,bar(Y)=8,sumx^(2)=28`, what will be the value of `sumy^(2)`? |
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Answer» `r=(sumxy)/(sqrt(sumx^(2)xxsumy^(2)))` Given : `r=0.997, sum xyl =46 , bar (X)=4, bar (Y)=8, sum x^(2)=28` Substituting the values, we get `0.997=(46)/(sqrt(28xx sumy^(2)))` Squaring both side , we get `0.994=(2,116)/(28xxsumy^(2))` `implies 27.832xx sumy^(2)=2,116` `sumy^(2)=76.03` Value of `sumy^(2)=76.03` |
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| 21. |
What is maent by correlation ? Explain its various kinds. |
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Answer» When the relationship of a quantitative nature, the appropriate statistical tool for discovering and measuring the relationship and expressing it in a brief formula is known as correlation. Various kinds of correlation are: i) Positive correlation: When two variables move in the same direction, that is one increases the other also increases and when one decreases the other also decreases, such a relation is called positive correlation. ii) Negative Correlation: When two variables change in different directions, it is called negative correlation. iii) Linear Correlation: When two variables change in constant proportion, it is called linear correlation. iv) Non-linear Correlation: When the variables do not change in any constant proportion, the relationship is said to be non-linear. |
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| 22. |
Definite relation between two or more than two groups or series is called correlation. (true/false) |
| Answer» Correct Answer - True | |
| 23. |
From the data given below, find the number of items (N), r=0.5,`sumxy=120`, Standard Deviation of `Y(sigma_(y))=8,sumx^(2)=90` where , x and y are deviations from arithmetic mean. |
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Answer» Given `: r=0.5,sumxy=120,sumx^(2)=90, sigma_(y)=8` Now, ` sigma_(y)=sqrt((sumy^(2))/(N))` when `y=Y-bar(Y)` [formula of Standard Deviation ] `8=sqrt((sumy^(2))/(N))` Squaring both sides, we get `64=(sumy^(2))/(N) implies sumy^(2)=64N` Now, `r=(sumxy)/(sqrt(sumx^(2)xxsumy^(2)))` `implies 0.5=(120)/(sqrt(90xx64N))` Squaring both sides `0.25=((120)^(2))/(90xx64N)` `implies0.25=(14,400)/(5,760 N)` `implies (0.25)(5,760)N=14,400` `implies(1,440)N=14,400` `:. N=(14,400)/(1,440)=10` Number of Items=10 |
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| 24. |
State the properties of correlation cofficient. |
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Answer» Properties of Correlation coefficient are:i) r has no unit. It is a pure number. It means units of measurement are not parts of r. ii) A negative value of r indicates an inverse relation, and if r is positive, the two variables move in the same direction. iii)If r= 0, the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there. iv) If r= 1 or r= -1, the correlation is perfect or proportionate. A high value of r indicates strong linear relationship i.e., +1 or -1. v) The value of the correlation coefficient lies between minus one and plus one. If the value of r lies outside this range, it indicates error in the calculation. |
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| 25. |
Explain the various kinds of correlation . |
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Answer» The various kinds of correlation are:1. Positive, Negative or Zero Correlation:When the increase in one variable (X) is followed by a corresponding increase in the other variable (Y); the correlation is said to be positive correlation. The positive correlations range from 0 to +1; the upper limit i.e. +1 is the perfect positive coefficient of correlation. If, on the other hand, the increase in one variable (X) results in a corresponding decrease in the other variable (Y), the correlation is said to be negative correlation.The negative correlation ranges from 0 to – 1; the lower limit giving the perfect negative correlation. The perfect negative correlation indicates that for every unit increase in one variable, there is proportional unit decrease in the other. Zero correlation means no relationship between the two variables X and Y; i.e. the change in one variable (X) is not associated with the change in the other variable (Y). For example, body weight and intelligence, shoe size and monthly salary; etc. The zero correlation is the mid-point of the range – 1 to + 1. ii) Linear or Curvilinear Correlation:Linear correlation is the ratio of change between the two variables either in the same direction or opposite direction and the graphical representation of the one variable with respect to other variable is straight line.Consider another situation. First, with increase of one variable, the second variable increases proportionately upto some point; after that with an increase in the first variable the second variable starts decreasing. |
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| 26. |
What kind of relationship between X and Y is indicated , if the points of the scattered diagram tend to cluster about (i) a straight line parallel to the X-axis (ii) a straight line parallel to the Y-axis (iii) a straight line sloping upward ,and (iv) straight line sloping downward ? |
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Answer» i) If the points of the scattered diagram tend to cluster about a straight line parallel to the X-axis, there is no correlation between X and Y. ii) If the points of the scattered diagram tend to cluster about a straight line parallel to the Y-axis, there is no correlation between X and Y. iii) If the points of the scattered diagram tend to cluster about a straight line sloping upward, then there is a case of perfect positive correlation between X and Y. iv) If the points of the scattered diagram tend to cluster about a straight line sloping downward, then there exists perfect negative correlation between X and Y. |
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| 27. |
Correlation is a statistical technique that measures _____________ relationship between different variables. (quantitative/qualitative) |
| Answer» Correct Answer - quantitative | |
| 28. |
In the step-deviation method of estimating standard deviation, deviations are taken from the ____________ (actual average/assumed average) |
| Answer» Correct Answer - assumed average | |
| 29. |
Explain the scattered diagram method of correlation. |
| Answer» Scattered diagram offers a graphic expression of the direction and degree of correlation. To make a scattered diagram, data are plotted on a graph paper. A dot is marked for each value. The course of these dots would indicate direction and closeness of the variables. | |
| 30. |
In case of positive correlation , two variables move in the _________direction. (same/opposite) |
| Answer» Correct Answer - same | |
| 31. |
Whien two variables change in a constant proportion, it is called :A. linear correlationB. non-linear correlationC. partial correlationD. none of these |
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Answer» Correct Answer - A A |
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| 32. |
___________offers a graphic expression of the direction and degree of correlation. (scattered diagram /Rank correlation) |
| Answer» Correct Answer - scattered diagram | |
| 33. |
In case of ___________correlation, two variables change in a constant proportion. (linear/non-linear) |
| Answer» Correct Answer - linear | |
| 34. |
If the value of cofficient of correlation is +1, it implies that correlation between the two variables is perfectly positive. (true/false) |
| Answer» Correct Answer - True | |
| 35. |
When the relation between two variables is studied simultaneously, it is called _________correlation. (simple/multiple) |
| Answer» Correct Answer - simple | |
| 36. |
If r = 0 , two variables are _________. (correlated/uncorrelated) |
| Answer» Correct Answer - uncorrelated | |
| 37. |
When two variables change in the same direction, then such a collertion is called :A. negativeB. positiveC. no correlationD. all of above |
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Answer» Correct Answer - B B |
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| 38. |
Calculate rank correlation coefficient whose marks in statistics and economics are given as follows:Stats: 41 45 70 45 30 67 70Eco: 40 55 47 65 55 71 55Rank in stats: 6, 4.5 , 1.5, 4.5, 7, 3, 1.5Rank in eco: 7 4 6 2 4 1 4 |
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Answer»
We have \(\sum\)di2 = 47, n = 7 Spearman's rank correction coefficient = \(\cfrac{1-6\sum d_i^2}{n(n^2-1)}\) = \(\cfrac{1-6\times47}{7(7^2-1)}\) = \(\cfrac{1-282}{336}\) = 0.1607 |
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| 39. |
Distinguish between simple and multiple correlations. |
| Answer» The correlation is said to be simple when only two variables are studied.The correlation is either multiple or partial when three or more variables are studied. The correlation is said to be Multiple when three variables are studied simultaneously. | |
| 40. |
Distinguish between positive and negative correlations. |
| Answer» The direction of a correlation is either positive or negative. In a negative correlation, the variables move in inverse, or opposite, directions. In other words, as one variable increases, the other variable decreases. When two variables have a positive correlation, it means the variables move in the same direction. | |
| 41. |
The lines of regression of X on Y estimates: (a) X for a given value of Y (b) Y for a given value of X (c) X from Y and Y from X(d) none of these |
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Answer» (a) X for a given value of Y |
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| 42. |
Scatter diagram of the variate values (X, Y) give the idea about:(a) functional relationship (b) regression model (c) distribution of errors (d) no relation |
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Answer» (a) functional relationship |
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| 43. |
The person suggested a mathematical method for measuring the magnitude of the linear relationship between two variables say X and Y is: (a) Karl Pearson (b) Spearman (c) Croxton and Cowden (d) Ya Lun Chou |
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Answer» (a) Karl Pearson |
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| 44. |
If two variables move in a decreasing direction then the correlation is: (a) positive(b) negative (c) perfect negative (d) no correlation |
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Answer» (a) positive |
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| 45. |
An example of a positive correlation is: (a) Income and expenditure (b) Price and demand (c) Repayment period and EMI(d) Weight and Income |
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Answer» (a) Income and expenditure |
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| 46. |
If r(X, Y) = 0 the variables X and Y are said to be: (a) Positive correlation (b) Negative correlation (c) No correlation (d) Perfect positive correlation |
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Answer» (c) No correlation |
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| 47. |
The correlation coefficient is:(a) r(X, Y) = \(\frac{\sigma\,_x\sigma\,_y}{cov(x,y)}\)(b) r(X, Y) = \(\frac{cov(x,y)}{\sigma\,_x\sigma\,_y}\)(c) r(X, Y) = \(\frac{cov(x,y)}{\sigma\,_y}\)(d) r(X, Y) = \(\frac{cov(x,y)}{\sigma\,_x}\) |
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Answer» (b) r(X, Y) = \(\frac{cov(x,y)}{\sigma\,_x\sigma\,_y}\) |
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