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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-15-CT
Linear Regression — Full Chapter Test
Chapter: Linear Regression
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
Both regression lines pass through:
  • A.the origin
  • B.$(\bar x,\bar y)$
  • C.$(0,1)$
  • D.no common point
2.
$b_{yx}\cdot b_{xy}$ equals:
  • A.$r$
  • B.$r^2$
  • C.$2r$
  • D.$1$
3.
To predict $y$ from $x$, use the line of:
  • A.$x$ on $y$
  • B.$y$ on $x$
  • C.either
  • D.best fit only
4.
If $b_{yx}=0.8,\ b_{xy}=0.2$, then $r=$
  • A.$0.16$
  • B.$0.4$
  • C.$1$
  • D.$0.5$
5.
If $y=2x+3$ (y on x), then at $x=5$, $y=$
  • A.$10$
  • B.$13$
  • C.$8$
  • D.$5$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
The regression line of $y$ on $x$ is $y=2x+3$. Predict $y$ when $x=5$.
7.
If $b_{yx}=0.8,\ b_{xy}=0.2$, find $r$.
8.
The regression line of $x$ on $y$ is $x=0.5y+2$. Predict $x$ when $y=4$.
9.
If $b_{yx}=-0.6,\ b_{xy}=-0.6$, find $r$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
The two regression lines are $2x+3y=8$ and $x+2y=5$. Find $\bar x$ and $\bar y$.
11.
If $b_{yx}=0.9,\ b_{xy}=0.4$, find $r$.
12.
The regression line of $y$ on $x$ is $3x+2y=26$ and $\bar x=4$. Find $\bar y$.
13.
If $r=0.6,\ \sigma_x=3,\ \sigma_y=5$, find $b_{yx}$ and $b_{xy}$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The two regression lines are $8x-10y+66=0$ and $40x-18y-214=0$. Find $\bar x$ and $\bar y$.
15.
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 $x$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $(\bar x,\bar y)$
  2. (B) $r^2$
  3. (B) $y$ on $x$
  4. (B) $0.4$
  5. (B) $13$
Section B — Short Answer (2 marks)
  1. $13$.
  2. $0.4$.
  3. $4$.
  4. $-0.6$.
Section C — Short Answer (3 marks)
  1. $\bar x=1,\ \bar y=2$.
  2. $0.6$.
  3. $\bar y=7$.
  4. $b_{yx}=1,\ b_{xy}=0.36$.
Section D — Long Answer (5 marks)
  1. $\bar x=13,\ \bar y=17$.
  2. $r=0.6$; line $y=0.8x+1.4$.
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