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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-15-COE-01
Regression Coefficients & Correlation — Assignment
Chapter: Linear Regression
Topic: Regression Coefficients & Correlation
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$b_{yx}\cdot b_{xy}$ equals:
  • A.$r$
  • B.$r^2$
  • C.$2r$
  • D.$1$
2.
If $b_{yx}=0.8,\ b_{xy}=0.2$, then $r=$
  • A.$0.16$
  • B.$0.4$
  • C.$1$
  • D.$0.5$
3.
The sign of $r$ is:
  • A.always positive
  • B.same as the regression coefficients
  • C.opposite to them
  • D.always negative
4.
Which pair is impossible as regression coefficients?
  • A.$0.8,0.2$
  • B.$-0.6,-0.6$
  • C.$2,3$
  • D.$0.5,0.5$
5.
$b_{yx}=$
  • A.$r\dfrac{\sigma_y}{\sigma_x}$
  • B.$r\dfrac{\sigma_x}{\sigma_y}$
  • C.$\dfrac{r}{\sigma_x}$
  • D.$r\sigma_x\sigma_y$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $b_{yx}=0.8,\ b_{xy}=0.2$, find $r$.
7.
If $b_{yx}=-0.6,\ b_{xy}=-0.6$, find $r$.
8.
Can $b_{yx}=2$ and $b_{xy}=3$ both be regression coefficients?
9.
If $r=0.5,\ \sigma_y=4,\ \sigma_x=2$, find $b_{yx}$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $b_{yx}=0.9,\ b_{xy}=0.4$, find $r$.
11.
If $r=0.6,\ \sigma_x=3,\ \sigma_y=5$, find $b_{yx}$ and $b_{xy}$.
12.
If one regression coefficient is $1.6$, can the other be $0.8$?
13.
If $b_{yx}=-0.4,\ b_{xy}=-0.9$, find $r$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
For a data set, $b_{yx}=0.8,\ b_{xy}=0.45$ and $\bar x=2,\ \bar y=3$. Find $r$ and the regression line of $y$ on $x$.
15.
The regression coefficients are $b_{yx}=1.2$ and $b_{xy}=0.6$. Are they possible? Find $r$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $r^2$
  2. (B) $0.4$
  3. (B) same as the regression coefficients
  4. (C) $2,3$
  5. (A) $r\dfrac{\sigma_y}{\sigma_x}$
Section B — Short Answer (2 marks)
  1. $0.4$.
  2. $-0.6$.
  3. No.
  4. $1$.
Section C — Short Answer (3 marks)
  1. $0.6$.
  2. $b_{yx}=1,\ b_{xy}=0.36$.
  3. No (product $>1$).
  4. $-0.6$.
Section D — Long Answer (5 marks)
  1. $r=0.6$; line $y=0.8x+1.4$.
  2. Possible; $r=\sqrt{0.72}\approx0.85$.
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