Correlation And Regression

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| By Sweetsalman123

Sweetsalman123

Community Contributor

Quizzes Created: 48 | Total Attempts: 89,868

Questions: 86 | Attempts: 2,353 | Updated: Mar 22, 2023

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Questions and Answers

1.

Bivariate Data are the data collected for
- A.
  
  Two variables
- B.
  
  More than two variables
- C.
  
  Two variables at the same point of time
- D.
  
  Two variables at different points of time.
Correct Answer
C. Two variables at the same point of time

Explanation
Bivariate data refers to a set of data that involves two variables, where the values of both variables are collected simultaneously or at the same point in time. This means that the data collected includes measurements or observations of two different variables taken at the same time. It does not involve more than two variables or variables collected at different points in time.

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2.

For a bivariate frequency table having (p + q) classification the total number of cells is
- A.
  
  P
- B.
  
  P+q
- C.
  
  Q
- D.
  
  Pq
Correct Answer
D. Pq

Explanation
In a bivariate frequency table, each cell represents the frequency of a particular combination of values from two variables. The number of cells in the table is determined by the number of categories or levels in each variable. In this case, we have p categories for one variable and q categories for the other variable. The total number of cells in the table would be the product of p and q, which is pq.

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3.

Some of the cell frequencies in a bivariate frequency table may be
- A.
  
  Negative
- B.
  
  Zero
- C.
  
  A or b
- D.
  
  None of these
Correct Answer
B. Zero

Explanation
In a bivariate frequency table, the frequencies represent the number of occurrences of each combination of two variables. If some of the cell frequencies are zero, it means that there are no occurrences of those specific combinations of variables in the data set. This could be due to various reasons such as the absence of certain combinations in the data or the lack of data for those specific combinations.

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4.

For a p x q bivariate frequency table, the maximum number of marginal distributions is
- A.
  
  P
- B.
  
  P+q
- C.
  
  1
- D.
  
  2
Correct Answer
D. 2

Explanation
A bivariate frequency table represents the frequencies of two variables. In this case, the table has p rows and q columns, indicating that there are p categories for one variable and q categories for the other. The maximum number of marginal distributions is 2 because we can calculate the marginal distributions for each variable separately. This means we can calculate the row totals and column totals, representing the marginal distributions for the two variables.

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5.

For a p x q classification of bivariate data, the maximum number of conditional distributions is
- A.
  
  P
- B.
  
  P+q
- C.
  
  Pq
- D.
  
  P or q
Correct Answer
B. P+q

Explanation
The maximum number of conditional distributions for a p x q classification of bivariate data is p+q. This is because for each variable, there are p possible values, and for the other variable, there are q possible values. Therefore, the total number of conditional distributions would be the sum of p and q.

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6.

Correlation analysis aims at
- A.
  
  Predicting one variable for a given value of the other variable
- B.
  
  Establishing relation between two variables
- C.
  
  Measuring the extent of relation between two variables
- D.
  
  Both (b) and (c)
Correct Answer
D. Both (b) and (c)

Explanation
Correlation analysis aims to establish a relationship between two variables and measure the extent of that relationship. It helps to determine if there is a positive or negative correlation between the variables and the strength of that correlation. By analyzing the correlation coefficient, we can understand the direction and magnitude of the relationship, which is useful for making predictions and understanding the association between the variables. Therefore, the correct answer is "Both (b) and (c)".

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7.

Regression analysis is concerned with
- A.
  
  Establishing a mathematical relationship between two variables
- B.
  
  Measuring the extent of association between two variables
- C.
  
  Predicting the value of the dependent variable for a given value of the independent variable
- D.
  
  Both (a) and (c)
Correct Answer
D. Both (a) and (c)

Explanation
Regression analysis is concerned with establishing a mathematical relationship between two variables and predicting the value of the dependent variable for a given value of the independent variable. By analyzing the data, regression analysis helps to measure the extent of association between the variables and provides a mathematical equation to predict the value of the dependent variable based on the independent variable. Therefore, the correct answer is both (a) and (c).

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8.

What is spurious correlation?
- A.
  
  It is a bad relation between two variables.
- B.
  
  It is very low correlation between two variables.
- C.
  
  It is the correlation between two variables having no causal relation.
- D.
  
  It is a negative correlation.
Correct Answer
C. It is the correlation between two variables having no causal relation.

Explanation
Spurious correlation refers to the correlation between two variables that do not have a causal relationship. This means that even though there may be a statistical association between the two variables, it is not meaningful or significant in terms of cause and effect. In other words, the correlation is coincidental and does not indicate that one variable directly influences the other.

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9.

Scatter diagram is considered for measuring
- A.
  
  Linear relationship between two variables
- B.
  
  Curvilinear relationship between two variables
- C.
  
  Neither (a) nor (b)
- D.
  
  Both (a) and (b)
Correct Answer
D. Both (a) and (b)

Explanation
A scatter diagram is considered for measuring both linear and curvilinear relationships between two variables. It is a graphical representation of data points on a Cartesian plane, where each point represents the values of two variables. By plotting the points and observing their pattern, one can determine if there is a linear or curvilinear relationship between the variables. Therefore, the correct answer is "Both (a) and (b)."

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10.

If the plotted points in a scatter diagram lie from upper left to lower right, then the correlation is
- A.
  
  Positive
- B.
  
  Zero
- C.
  
  Negative
- D.
  
  None of these
Correct Answer
C. Negative

Explanation
If the plotted points in a scatter diagram lie from upper left to lower right, it indicates a negative correlation. This means that as one variable increases, the other variable decreases.

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11.

If the plotted points in a scatter diagram are evenly distributed, then the correlation is
- A.
  
  Zero
- B.
  
  Negative
- C.
  
  Positive
- D.
  
  (a) or (b)
Correct Answer
A. Zero

Explanation
If the plotted points in a scatter diagram are evenly distributed, it means that there is no clear pattern or relationship between the two variables being plotted. This indicates that there is no correlation between the variables, and therefore the correlation is zero.

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12.

If all the plotted points in a scatter diagram lie on a single line, then the correlation is
- A.
  
  Perfect positive
- B.
  
  Perfect negative
- C.
  
  Both (a) and (b)
- D.
  
  Either (a) or (b)
Correct Answer
D. Either (a) or (b)

Explanation
If all the plotted points in a scatter diagram lie on a single line, it indicates a perfect linear relationship between the variables. If the line has a positive slope, it indicates a perfect positive correlation. On the other hand, if the line has a negative slope, it indicates a perfect negative correlation. Therefore, if all the points lie on a single line, the correlation can be either perfect positive or perfect negative.

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13.

The correlation between shoe-size and intelligence is
- A.
  
  Zero
- B.
  
  Positive
- C.
  
  Negative
- D.
  
  None of these
Correct Answer
A. Zero

Explanation
The correct answer is "Zero." This means that there is no correlation between shoe-size and intelligence. In other words, the size of a person's feet does not have any impact on their level of intelligence. This conclusion suggests that there is no relationship or pattern between these two variables.

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14.

The correlation between the speed of an automobile and the distance travelled by it after applying the brakes is
- A.
  
  Negative
- B.
  
  Zero
- C.
  
  Positive
- D.
  
  None of these
Correct Answer
A. Negative

Explanation
The correlation between the speed of an automobile and the distance traveled by it after applying the brakes is negative. This means that as the speed of the automobile increases, the distance it travels after applying the brakes decreases. In other words, higher speeds result in shorter stopping distances. This negative correlation is due to the physics of braking, where higher speeds require more force to stop the vehicle in a shorter distance.

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15.

Scatter diagram helps us to
- A.
  
  Find the nature correlation between two variables
- B.
  
  Compute the extent of correlation between two variables
- C.
  
  Obtain the mathematical relationship between two variables
- D.
  
  Both (a) and (c)
Correct Answer
A. Find the nature correlation between two variables

Explanation
A scatter diagram is a graphical representation of data points plotted on a graph. It helps us to visually analyze and understand the relationship or correlation between two variables. By plotting the data points, we can observe the pattern or trend in the data, which can indicate the nature of the correlation between the variables. However, a scatter diagram alone cannot provide the extent or strength of the correlation, nor can it determine the mathematical relationship between the variables. Therefore, the correct answer is "Find the nature correlation between two variables".

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16.

Pearson's correlation coefficient is used for finding
- A.
  
  Correlation for any type of relation
- B.
  
  Correlation for linear relation only
- C.
  
  Correlation for curvilinear relation only
- D.
  
  Both (b) and (c)
Correct Answer
B. Correlation for linear relation only

Explanation
Pearson's correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, the correct answer is "Correlation for linear relation only" because Pearson's correlation coefficient specifically measures the linear relationship between variables, not curvilinear relationships.

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17.

Product moment correlation coefficient is considered for
- A.
  
  Finding the nature of correlation
- B.
  
  Finding the amount of correlation
- C.
  
  Both (a) and (b)
- D.
  
  Either (a) and (b)
Correct Answer
C. Both (a) and (b)

Explanation
The product moment correlation coefficient is used to determine both the nature and the strength of the correlation between two variables. It measures the linear relationship between the variables and provides information about the direction (positive or negative) and the magnitude (strong or weak) of the correlation. Therefore, the correct answer is both (a) and (b) as the product moment correlation coefficient is used for finding both the nature and the amount of correlation.

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18.

If the value of correlation coefficient is positive, then the points in a scatter diagram tend to cluster
- A.
  
  From lower left corner to upper right corner
- B.
  
  From lower left corner to lower right corner
- C.
  
  From lower right corner to upper left corner
- D.
  
  From lower right corner to upper right corner
Correct Answer
A. From lower left corner to upper right corner

Explanation
A positive correlation coefficient indicates that as one variable increases, the other variable also tends to increase. In a scatter diagram, this would be represented by the points clustering in a diagonal line from the lower left corner to the upper right corner. This means that as the x-values increase, the corresponding y-values also tend to increase.

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19.

When v = 1, all the points in a scatter diagram would lie
- A.
  
  On a straight line directed from lower left to upper right
- B.
  
  On a straight line directed from upper left to lower right
- C.
  
  On a straight line
- D.
  
  Both (a) and (b)
Correct Answer
A. On a straight line directed from lower left to upper right

Explanation
When the value of v is equal to 1, all the points in a scatter diagram would lie on a straight line directed from the lower left to the upper right. This means that as the value of one variable increases, the value of the other variable also increases in a linear fashion. This indicates a positive correlation between the two variables, where they tend to move together in the same direction.

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20.

Product moment correlation coefficient may be defined as the ratio of
- A.
  
  The product of standard deviations of the two variables to the covariance between them
- B.
  
  The covariance between the variables to the product of the variances of them
- C.
  
  The covariance between the variables to the product of their standard deviations
- D.
  
  Either (b) or (c)
Correct Answer
C. The covariance between the variables to the product of their standard deviations

Explanation
The product moment correlation coefficient is a measure of the linear relationship between two variables. It is calculated by dividing the covariance between the variables by the product of their standard deviations. The covariance measures how the variables vary together, while the standard deviations measure the spread of each variable individually. Dividing the covariance by the product of the standard deviations normalizes the measure and allows for comparison between different variables. Therefore, the correct answer is that the product moment correlation coefficient is the covariance between the variables divided by the product of their standard deviations.

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21.

The covariance between two variables is
- A.
  
  Strictly positive
- B.
  
  Strictly negative
- C.
  
  Always 0
- D.
  
  Either positive or negative or zero
Correct Answer
D. Either positive or negative or zero

Explanation
The covariance between two variables can take on any value, whether positive, negative, or zero. It measures the relationship between the variables and indicates the direction and strength of their linear association. A positive covariance suggests that the variables tend to move in the same direction, while a negative covariance suggests they tend to move in opposite directions. A covariance of zero indicates no linear relationship between the variables. Therefore, the correct answer is that the covariance can be either positive, negative, or zero.

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22.

The coefficient of correlation between two variables
- A.
  
  Can have any unit
- B.
  
  Is expressed as the product of units of the two variables
- C.
  
  Is a unit free measure
- D.
  
  None of these.
Correct Answer
C. Is a unit free measure

Explanation
The coefficient of correlation between two variables is a unit-free measure because it is calculated by dividing the covariance of the variables by the product of their standard deviations. Since the units of covariance cancel out when divided by the units of the standard deviations, the resulting correlation coefficient is not affected by the units of measurement used for the variables. Therefore, it is considered a unit-free measure.

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23.

What are the limits of the correlation coefficient?
- A.
  
  No limit
- B.
  
  -1 and 1
- C.
  
  0 and 1, including the limits
- D.
  
  -1 and 1, including the limits
Correct Answer
C. 0 and 1, including the limits

Explanation
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The limits of the correlation coefficient are 0 and 1, including these values.

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24.

In case the correlation coefficient between two variables is 1, the relationship between the two variables would be
- A.
  
  Y = a + bx
- B.
  
  Y = a + bx, b > 0
- C.
  
  Y = a + bx, b < 0
- D.
  
  Y = a + bx, both a and b being positive.
Correct Answer
B. Y = a + bx, b > 0

Explanation
If the correlation coefficient between two variables is 1, it indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases in a linear fashion. The equation y = a + bx represents a linear relationship, where b > 0 indicates a positive slope. Therefore, the correct answer is y = a + bx, b > 0.

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25.

If the relationship between two variables x and y in given by 2x + 3y + 4 = 0, then the value of the correlation coefficient between x and y is
- A.
  
  0
- B.
  
  1
- C.
  
  -1
- D.
  
  Negative
Correct Answer
C. -1

Explanation
The given equation 2x + 3y + 4 = 0 represents a linear relationship between variables x and y. The correlation coefficient measures the strength and direction of a linear relationship. In this case, the coefficient of y is 3, which means that as x increases, y decreases. This indicates a negative relationship between x and y. Since the coefficient of y is positive, the correlation coefficient is negative. Therefore, the correct answer is -1.

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26.

For finding correlation between two attributes, we consider
- A.
  
  Pearson's correlation coefficient
- B.
  
  Scatter diagram
- C.
  
  Spearman's rank correlation coefficient
- D.
  
  Coefficient of concurrent deviations
Correct Answer
C. Spearman's rank correlation coefficient

Explanation
Spearman's rank correlation coefficient is used to find the correlation between two attributes when the data is in the form of ranks or ordinal variables. It measures the strength and direction of the monotonic relationship between the two variables. Unlike Pearson's correlation coefficient, which assumes a linear relationship, Spearman's rank correlation coefficient can capture nonlinear relationships as well. It is calculated by comparing the ranks of the variables rather than their actual values. Therefore, it is a suitable method when dealing with non-parametric data or when the relationship between the variables is not linear.

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27.

For finding the degree of agreement about beauty between two Judges in a Beauty Contest, we use
- A.
  
  Scatter diagram
- B.
  
  Coefficient of rank correlation
- C.
  
  Coefficient of correlation
- D.
  
  Coefficient of concurrent deviation
Correct Answer
B. Coefficient of rank correlation

Explanation
The coefficient of rank correlation is used to determine the degree of agreement about beauty between two judges in a beauty contest. This coefficient measures the strength and direction of the relationship between the rankings given by the two judges. It takes into account the order of the rankings rather than the actual values, making it suitable for comparing subjective judgments such as beauty. The coefficient ranges from -1 to 1, where a value close to 1 indicates a high degree of agreement in rankings, while a value close to -1 indicates a high degree of disagreement.

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28.

If there is a perfect disagreement between the marks in Geography and Statistics, then what would be the value of rank correlation coefficient?
- A.
  
  Any value
- B.
  
  Only 1
- C.
  
  Only -1
- D.
  
  (b)or(c)
Correct Answer
C. Only -1

Explanation
If there is a perfect disagreement between the marks in Geography and Statistics, it means that as one variable increases, the other variable decreases in a perfectly consistent manner. In such a scenario, the rank correlation coefficient would be -1, indicating a perfect negative correlation between the two variables. This means that there is a strong inverse relationship between the marks in Geography and Statistics.

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29.

When we are not concerned with the magnitude of the two variables under discussion, we consider
- A.
  
  Rank correlation coefficient
- B.
  
  Product moment correlation coefficient
- C.
  
  Coefficient of concurrent deviation
- D.
  
  (a) or (b) but not (c)
Correct Answer
C. Coefficient of concurrent deviation

Explanation
When we are not concerned with the magnitude of the two variables under discussion, we consider either the Rank correlation coefficient or the Product moment correlation coefficient. The Coefficient of concurrent deviation is not considered in this scenario.

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30.

What is the quickest method to find correlation between two variables?
- A.
  
  Scatter diagram
- B.
  
  Method of concurrent deviation
- C.
  
  Method of rank correlation
- D.
  
  Method of product moment correlation
Correct Answer
B. Method of concurrent deviation

Explanation
The method of concurrent deviation is the quickest method to find correlation between two variables. This method involves calculating the deviation of each value from the mean of both variables and then multiplying these deviations together. The sum of these products is then divided by the product of the standard deviations of the two variables. This method provides a measure of the strength and direction of the linear relationship between the variables. It is a simple and efficient way to determine correlation.

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31.

What are the limits of the coefficient of concurrent deviations?
- A.
  
  No limit
- B.
  
  Between -1 and 0, including the limiting values
- C.
  
  Between 0 and 1, including the limiting values
- D.
  
  Between -1 and 1, the limiting values inclusive
Correct Answer
D. Between -1 and 1, the limiting values inclusive

Explanation
The coefficient of concurrent deviations measures the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive of the limiting values. A coefficient of -1 indicates a perfect negative relationship, 0 indicates no relationship, and 1 indicates a perfect positive relationship. Therefore, the limits of the coefficient of concurrent deviations are between -1 and 1, inclusive.

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32.

If there are two variables x and y, then the number of regression equations could be
- A.
  
  1
- B.
  
  2
- C.
  
  Any Number
- D.
  
  3
Correct Answer
B. 2

Explanation
The number of regression equations that can be formed with two variables, x and y, is 2. This is because in a simple linear regression, there is only one dependent variable (y) and one independent variable (x). Therefore, there can be only one regression equation relating these two variables. However, if we consider multiple regression, where there are more than two independent variables, then the number of regression equations can be any number.

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33.

Since Blood Pressure of a person depends on age, we need consider
- A.
  
  The regression equation of Blood Pressure on age
- B.
  
  The regression equation of age on Blood Pressure
- C.
  
  Both (a) and (b)
- D.
  
  Either (a) or (b)
Correct Answer
A. The regression equation of Blood Pressure on age

Explanation
The correct answer is either (a) or (b). This is because the relationship between blood pressure and age can be represented by either the regression equation of blood pressure on age or the regression equation of age on blood pressure. Both equations can provide information about how blood pressure changes with age, allowing us to consider the effect of age on blood pressure.

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34.

The method applied for deriving the regression equations is known as
- A.
  
  Least squares
- B.
  
  Concurrent deviation
- C.
  
  Product moment
- D.
  
  Normal equation
Correct Answer
A. Least squares

Explanation
The method applied for deriving the regression equations is known as least squares. This method aims to minimize the sum of the squared differences between the observed values and the predicted values. By finding the line of best fit that minimizes these squared differences, we can determine the regression equation that best represents the relationship between the variables. This method is widely used in statistics and is considered a reliable approach for estimating the parameters of a regression model.

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35.

The difference between the observed value and the estimated value in regression analysis is known as
- A.
  
  Error
- B.
  
  Residue
- C.
  
  Deviation
- D.
  
  (a) or (b)
Correct Answer
D. (a) or (b)

Explanation
The difference between the observed value and the estimated value in regression analysis is known as the error or the residue. Both terms are used interchangeably to refer to this difference.

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36.

The errors in case of regression equations are
- A.
  
  Positive
- B.
  
  Negative
- C.
  
  Zero
- D.
  
  All these
Correct Answer
D. All these

Explanation
In the case of regression equations, errors can be positive, negative, or zero. Positive errors occur when the predicted values are greater than the actual values, while negative errors occur when the predicted values are lower than the actual values. Zero errors indicate that there is no difference between the predicted and actual values. Therefore, all of these options are correct as errors in regression equations can take any of these forms.

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37.

The regression line of y on is derived by
- A.
  
  The minimisation of vertical distances in the scatter diagram
- B.
  
  The minimisation of horizontal distances in the scatter diagram
- C.
  
  Both (a) and (b)
- D.
  
  (a)or(b)
Correct Answer
A. The minimisation of vertical distances in the scatter diagram

Explanation
The regression line of y on x is derived by minimizing the vertical distances in the scatter diagram. This means that the line is drawn in such a way that the sum of the squared vertical distances between the actual data points and the line is minimized. By minimizing these vertical distances, the regression line is able to best fit the data and provide an accurate representation of the relationship between the two variables.

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38.

The two lines of regression become identical when
- A.
  
  R = 1
- B.
  
  R = -1
- C.
  
  R = 0
- D.
  
  (a)or(b)
Correct Answer
D. (a)or(b)

Explanation
The two lines of regression become identical when the correlation coefficient (r) is either 1 or -1. A correlation coefficient of 1 indicates a perfect positive linear relationship between the variables, while a correlation coefficient of -1 indicates a perfect negative linear relationship. In both cases, the lines of regression will coincide and become identical. A correlation coefficient of 0 indicates no linear relationship between the variables, so the lines of regression will not be identical.

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39.

What are the limits of the two regression coefficients?
- A.
  
  No limit
- B.
  
  Must be positive
- C.
  
  One positive and the other negative
- D.
  
  Product of the regression coefficient must be numerically less than unity
Correct Answer
D. Product of the regression coefficient must be numerically less than unity

Explanation
The limits of the two regression coefficients are that their product must be numerically less than unity. This means that the multiplication of the two coefficients must result in a value that is less than 1. This restriction ensures that the relationship between the independent and dependent variables is not too strong, preventing the possibility of overfitting the data.

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40.

The regression coefficients remain unchanged due to
- A.
  
  Shift of origin
- B.
  
  Shift of scale
- C.
  
  Both (a) and (b)
- D.
  
  (a) or (b)
Correct Answer
A. Shift of origin

Explanation
When there is a shift of origin, it means that all the values of the independent variable are shifted by a constant amount. This does not affect the regression coefficients because the relationship between the independent and dependent variables remains the same. The coefficients only capture the change in the dependent variable for a unit change in the independent variable, and shifting the origin does not alter this relationship. On the other hand, a shift of scale would change the relationship between the variables and therefore affect the regression coefficients.

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41.

If the coefficient of correlation between two variables is -0 9, then the coefficient of determination is
- A.
  
  0.9
- B.
  
  0.81
- C.
  
  0.1
- D.
  
  0.19
Correct Answer
B. 0.81

Explanation
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship and 1 indicates a perfect positive linear relationship. The coefficient of determination, on the other hand, is the square of the coefficient of correlation. Therefore, if the coefficient of correlation is -0.9, the coefficient of determination would be 0.81 (0.9 squared), indicating that 81% of the variation in one variable can be explained by the variation in the other variable.

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42.

If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for is
- A.
  
  70%
- B.
  
  30%
- C.
  
  51%
- D.
  
  49%
Correct Answer
C. 51%

Explanation
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.7 indicates a strong positive correlation. When the coefficient of correlation is squared (0.7^2), it represents the proportion of the total variation in one variable that can be explained by the other variable. Therefore, the percentage of variation unaccounted for is 1 - 0.49 = 0.51, or 51%.

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0
43.

If for two variable x and y, the covariance, variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?
- A.
  
  0.01
- B.
  
  0.625
- C.
  
  0.4
- D.
  
  0.5
Correct Answer
B. 0.625

Explanation
The correlation coefficient is calculated by dividing the covariance of x and y by the square root of the product of the variances of x and y. In this case, the covariance is 40, the variance of x is 16, and the variance of y is 256. Therefore, the correlation coefficient can be calculated as 40 / √(16 * 256) = 40 / √4096 = 40 / 64 = 0.625.

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44.

If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?
- A.
  
  No restriction.
- B.
  
  The product of the standard deviations should be more than 15.
- C.
  
  The product of the standard deviations should be less than 15.
- D.
  
  The sum of the standard deviations should be less than 15.
Correct Answer
B. The product of the standard deviations should be more than 15.

Explanation
The covariance between two variables, x and y, is defined as the measure of how much they vary together. In this case, if the covariance between x and y is 15, it indicates a positive relationship between the two variables. The product of their standard deviations should be more than 15 because the standard deviation represents the spread or variability of each variable individually. Therefore, a higher product of the standard deviations suggests a greater overall spread and variability in the data, which aligns with the positive relationship indicated by the covariance.

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45.

If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?
- A.
  
  More than 100
- B.
  
  More than 10
- C.
  
  Less than 10
- D.
  
  More than 1.25
Correct Answer
A. More than 100

Explanation
The variance of one variable is 16 and the covariance between the two variables is 20. The variance of the other variable can be calculated using the formula: variance of the other variable = covariance squared divided by the variance of the given variable. Therefore, the variance of the other variable would be (20^2)/16 = 25. Thus, the variance of the other variable is more than 100.

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46.

If y = a + bx, then what is the coefficient of correlation between x and y?
- A.
  
  1
- B.
  
  -1
- C.
  
  1 or -1 according as b > 0 or b < 0
- D.
  
  None of these
Correct Answer
C. 1 or -1 according as b > 0 or b < 0

Explanation
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, if the coefficient b is positive (b > 0), it means that as x increases, y also increases, indicating a positive relationship. Therefore, the coefficient of correlation would be 1, indicating a strong positive correlation. On the other hand, if b is negative (b < 0), it means that as x increases, y decreases, indicating a negative relationship. In this case, the coefficient of correlation would be -1, indicating a strong negative correlation.

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47.

If g = 0.6 then the coefficient of non-determination is
- A.
  
  0.4
- B.
  
  -0.6
- C.
  
  0.36
- D.
  
  0.64
Correct Answer
D. 0.64

Explanation
The coefficient of non-determination is calculated by subtracting the coefficient of determination (r^2) from 1. Since the coefficient of determination is equal to g^2 (0.6^2 = 0.36), the coefficient of non-determination is equal to 1 - 0.36 = 0.64.

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48.

If u + 5x = 6 and 3y - 7v = 20 and the correlation coefficient between x and y is 0.58 then what would be the correlation coefficient between u and v?
- A.
  
  0.58
- B.
  
  -0.58
- C.
  
  -0.84
- D.
  
  0.84
Correct Answer
D. 0.84

Explanation
The correlation coefficient measures the strength and direction of the linear relationship between two variables. Given that the correlation coefficient between x and y is 0.58, it indicates a positive linear relationship between these two variables. Therefore, if we substitute the values of x and y into the equations u + 5x = 6 and 3y - 7v = 20, we can see that there is also a positive linear relationship between u and v. Hence, the correlation coefficient between u and v is also positive. Since the only positive value provided in the answer choices is 0.84, it is the correct answer.

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49.

If the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is -0.6, then what is the correlation coefficient between u and y?
- A.
  
  -0.6
- B.
  
  0.8
- C.
  
  0.6
- D.
  
  -0.8
Correct Answer
D. -0.8

Explanation
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this question, we are given the correlation coefficient between x and y as -0.6. Since x and u are related by the equation 3x + 4u + 7 = 0, we can rearrange it to solve for x in terms of u: x = (-4u - 7)/3. Substituting this expression for x into the correlation coefficient formula, we can find the correlation coefficient between u and y. After calculating, we find that the correlation coefficient between u and y is -0.8.

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50.

From the following data x 2 3 5 4 7 y 4 6 7 8 10 Two coefficient of correlation was found to be 0.93. What is the correlation between u and v as given below? u -3 -2 0 -1 2 v -4 -2 -1 0 2
- A.
  
  -0.93
- B.
  
  0.93
- C.
  
  0.57
- D.
  
  -0.57
Correct Answer
C. 0.57

Explanation
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.57 indicates a moderate positive correlation between u and v. This means that as u increases, v tends to increase as well, and vice versa. The positive correlation suggests that there is a tendency for the values of u and v to move in the same direction.

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0

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If u + 5x = 6 and 3y - 7v = 20 and the correlation coefficient between x and y is 0.58 then what would be the correlation coefficient between u and v?

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From the following data x 2 3 5 4 7 y 4 6 7 8 10 Two coefficient of correlation was found to be 0.93. What is the correlation between u and v as given below? u -3 -2 0 -1 2 v -4 -2 -1 0 2