Which of the following values is not possible as a value of $r\ ?$
- A$0.99$
- ✓$-1.07$
- C$-0.85$
- D$0$
Answer: B.
View full solution →Question types
LINEAR CORRELATION question types
226 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
226
Questions
6
Question groups
5
Question types
01
MCQ
26 Q→021 Marks Each
44 Q→032 Marks Each
47 Q→043 Marks Each
36 Q→054 Marks Each
20 Q→065 Mark Each
53 Q→Sample Questions
LINEAR CORRELATION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What does the numerator indicate in the formula for calculating the correlation coefficient by Karl Pearson’s method ?
- AProduct of variance of $X$ and $Y$
- ✓Covariance of $X$ and $Y$
- CVariance of $X$
- DVariance of $Y$
Answer: B.
View full solution →Which kind of the correlation can be obtained if the two variables are varying in opposite direction in constant proportion ?
- APerfect Positive correlation
- ✓Partial Positive correlation
- CPerfect Negative correlation
- DPartial Negative correlation
Answer: B.
View full solution →The measurement unit of a variable ‘Weight’ is kg. and that of ‘Height’ is cm. What can you see about the measurement unit of the correlation coefficient between them ?
- Akg
- Bcm
- Ckm
- ✓does not have any unit
Answer: D.
View full solution →What is the range of the correlation coefficient $r ?$
- A$-1 < r < 1$
- B$0$ to $1$
- ✓$– 1 ≤ r ≤ 1$
- D$ – 1$ to $0$
Answer: C.
View full solution →If $r(x,y):0.3$ then find $r(u,v)$ for the following.
$u=\frac{20-x}{3}$ and $v=\frac{20-y}{7}$
View full solution →$u=\frac{20-x}{3}$ and $v=\frac{20-y}{7}$
If $r(x,y):0.3$ then find $r(u,v)$ for the following.
$u=\frac{5-x}{2}$ and $v=\frac{5+y}{2}$
View full solution →$u=\frac{5-x}{2}$ and $v=\frac{5+y}{2}$
If $r(x,y):0.3$ then find $r(u,v)$ for the following.
$u=\frac{2 x-3}{10}$ and $v=\frac{10-y}{100}$
View full solution →$u=\frac{2 x-3}{10}$ and $v=\frac{10-y}{100}$
If $r(x,y):0.3$ then find $r(u,v)$ for the following.
$u=\frac{x-5}{3}$ and $v=2 y+7$
View full solution →$u=\frac{x-5}{3}$ and $v=2 y+7$
If $r(x,y):0.3$ then find $r(u,v)$ for the following.
$u = 1-10$ and $v = y+10$
View full solution →$u = 1-10$ and $v = y+10$
if the correlation coefficient between two variables $X$ and $Y$ is $0.5,$ find the value of the following : $(i)\ r (x, - y)\ (ii)\ r (- x, y)\ (iii)\ r (- x, - y)$
View full solution →The following results are obtained from a bivariate data.
$n=10, \Sigma(x-\bar{x})(y-\bar{y})=72, s_{x}=3$ and $\Sigma(y-\bar{y})^{2}=160$ Find the correlation coefficient.
View full solution →$n=10, \Sigma(x-\bar{x})(y-\bar{y})=72, s_{x}=3$ and $\Sigma(y-\bar{y})^{2}=160$ Find the correlation coefficient.
Determine the value of the correlation coefficient from the following results.
$\operatorname{Cov}(x, y): s_{x}^{2}=3: 5$ and $s_{x}: s_{y}=1: 2$
View full solution →$\operatorname{Cov}(x, y): s_{x}^{2}=3: 5$ and $s_{x}: s_{y}=1: 2$
A transport company wants to know the relation between driving experience and the number of accidents by the drivers. The sum of squares of differences in the ranks given to driving experience and the number of accidents by eight drivers is found to be $126.$ Find the rank correlation coefficient.
View full solution →To study the relationship between the marks obtained in Statistics $(X)$ and marks in Economics $(Y)$ of the students of a school, a sample of ten students is taken and the following information is obtained.
$\Sigma(x-\bar{x})(y-\bar{y})=120, \Sigma(x-\bar{x})^{2}=80, \Sigma(y-\bar{y})^{2}=500$
Find the value of $r.$
View full solution →$\Sigma(x-\bar{x})(y-\bar{y})=120, \Sigma(x-\bar{x})^{2}=80, \Sigma(y-\bar{y})^{2}=500$
Find the value of $r.$
The singing talent of five singers $A, B, C, D$ and $E$ was judged by two judges in a singing competition. The ranks assigned to five singers are as follows.
Find the similarity between the decisions of the two judges from the rank correlation coefficient.
View full solution →Find the similarity between the decisions of the two judges from the rank correlation coefficient.
The principal of a school has conducted a test for five students selected in a sample to judge the relation between the knowledge of Mathematics and memory ability in the subject of History of the students. The ranks given to these five students in the subjects of Mathematics and History are given below. Find the rank correlation coefficient between ranks of two subjects using this information.
Seven employees are selected from a company. They are judged by two managers from the company in terms of their administrative skills. The ranks given by them are as follows.
Calculate the rank correlation coefficient between the judgments given by two managers.
Calculate the rank correlation coefficient between the judgments given by two managers.
To study the relationship between the sales and the profit of a company, the following information is obtained for the last six years.
$X$ Annual Sales $($lakh $₹)$
$Y$ Annual Profit $($ten thousand $₹)$
$n=6, \Sigma x=58, \Sigma y=40, \Sigma x y=431, \Sigma x^{2}=606, \Sigma y^{2}=316$
Find the correlation coefficient between $X$ and $Y.$
View full solution →$X$ Annual Sales $($lakh $₹)$
$Y$ Annual Profit $($ten thousand $₹)$
$n=6, \Sigma x=58, \Sigma y=40, \Sigma x y=431, \Sigma x^{2}=606, \Sigma y^{2}=316$
Find the correlation coefficient between $X$ and $Y.$
State the necessary precautions to be taken while interpreting the value of correlation coefficient.
To know the relation between the ability in two different subjects for the students, a sample of seven students is taken from a school. From the information of marks in two subjects for $'7$ students, it is known that the sum of the squares of differences in the ranks of these marks is $25.5.$ It is also known that two students got equal marks in one subject and all the remaining marks are different. Find the rank correlation coefficient.
View full solution →To study the relation between the age $(X$ years of teenage children and their daily requirement of protein $0*$ grams$),$ the following information is obtained from a sample of $10$ children taken by the Health Department of State.
$\Sigma x=140, \Sigma y=150, \Sigma(x-10)^{2}=180, \quad \Sigma(y-15)^{2}=215, \Sigma(x-10)(y-15)=60$
Find the correlation coefficient between $X$ and $Y.$
View full solution →$\Sigma x=140, \Sigma y=150, \Sigma(x-10)^{2}=180, \quad \Sigma(y-15)^{2}=215, \Sigma(x-10)(y-15)=60$
Find the correlation coefficient between $X$ and $Y.$
A project is conducted by the group of the students of an $MBA$ Institute to know the relation between the results of the final year of school and final year of graduation for the students. The following information is obtained from a sample of $10$ students regarding the percentage of marks in standard $12 (x)$ and the percentage of marks in the final year of graduation $(y).$
$n=10, \Sigma(x-65)=-2, \Sigma(y-60)=2, \Sigma(x-65)^{2}=176, \Sigma(y-60)^{2}=140, \Sigma(x-65)(y-60)=141$
Find the correlation coefficient between the percentages of marks in Standard $12$ and the final year of graduation.
View full solution →$n=10, \Sigma(x-65)=-2, \Sigma(y-60)=2, \Sigma(x-65)^{2}=176, \Sigma(y-60)^{2}=140, \Sigma(x-65)(y-60)=141$
Find the correlation coefficient between the percentages of marks in Standard $12$ and the final year of graduation.
An educationalist has conducted an experiment to know the relation between the usage of Social Media in mobile phone and the result of the examination. A group of $10$ students is selected for this and the following results were obtained regarding, the time spent $x ($in hours$)$ in last week on Social Media and the marks $(2)$ obtained out of $50$ in the examination, taken immediately after it.
$\Sigma x=133, \Sigma y=220, \Sigma x^{2}=2344, \Sigma y^{2}=6500$ and $\Sigma x y=3500$
Later on, it was found that one of the pairs of observations of $X$ and $Y$ was taken as $(13, 20)$ instead of $(15, 25) .$
Find the correct value of the correlation coefficient between $X$ and $Y.$
View full solution →$\Sigma x=133, \Sigma y=220, \Sigma x^{2}=2344, \Sigma y^{2}=6500$ and $\Sigma x y=3500$
Later on, it was found that one of the pairs of observations of $X$ and $Y$ was taken as $(13, 20)$ instead of $(15, 25) .$
Find the correct value of the correlation coefficient between $X$ and $Y.$
Ten students selected from various schools of a district were ranked on the basis of their proficiency in Sports and General knowledge. The rank correlation coefficient obtained from the data was found to be $0.2.$ Later on, it was noticed that the difference in the ranks of the two attributes for one of the students was taken as $3$ instead of $2.$ Find the correct value of rank correlation coefficient.
View full solution →To know the relation between the heights and weights of the students of a school, a sample of six students is taken and the following information is obtained. Find the correlation coefficient between the heights and weights of the students.
From the following information of weekly minimum temperature $($in Celsius$)$ and the sale $($in hundred units$)$ of heaters during a week in a city of North India for five weeks, calculate the correlation coefficient between minimum temperature and sale of heaters.
View full solution →The details of monthly sale of mobile phones $($in thousand units$)$ and its profit $($in lakh $₹)$ for the last six months for a company making mobile phones are given below.
Find the correlation coefficient between ‘number of mobile phones sold’ and its ‘profit’.
View full solution →Find the correlation coefficient between ‘number of mobile phones sold’ and its ‘profit’.
In order to study the relation between the performance of students of a school in terms of marks in the subjects of Gujarati and Statistics, the following data are collected by taking a sample of six students.
Compute the correlation coefficient between the marks obtained by the students in two subjects from this data.
Compute the correlation coefficient between the marks obtained by the students in two subjects from this data.
The following information is collected by taking a sample of seven candidates having nearly same intellectual ability to know the effect of ‘last days preparation’ for a competitive examination of general knowledge on the ‘result of the examination’.
Find the correlation coefficient between reading hours of the last three days and marks obtained in the examination from the data and interpret it.
Find the correlation coefficient between reading hours of the last three days and marks obtained in the examination from the data and interpret it.
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