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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-15-REG-01
Lines of Regression — Assignment
Chapter: Linear Regression
Topic: Lines of Regression
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.
Both regression lines pass through:
  • A.the origin
  • B.$(\bar x,\bar y)$
  • C.$(0,1)$
  • D.no common point
2.
To predict $y$ from $x$, use the line of:
  • A.$x$ on $y$
  • B.$y$ on $x$
  • C.either
  • D.best fit only
3.
If $y=2x+3$ (y on x), then at $x=5$, $y=$
  • A.$10$
  • B.$13$
  • C.$8$
  • D.$5$
4.
Solving the two regression lines simultaneously gives:
  • A.the slopes
  • B.$(\bar x,\bar y)$
  • C.the correlation
  • D.the variance
5.
The line of $y$ on $x$ is:
  • A.$y-\bar y=b_{yx}(x-\bar x)$
  • B.$x-\bar x=b_{xy}(y-\bar y)$
  • C.$y=x$
  • D.$y=r x$
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.
The regression line of $x$ on $y$ is $x=0.5y+2$. Predict $x$ when $y=4$.
8.
Through which point do both regression lines pass?
9.
To estimate $x$ from a known $y$, which line is used?
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.
The regression line of $y$ on $x$ is $3x+2y=26$ and $\bar x=4$. Find $\bar y$.
12.
The regression line of $y$ on $x$ is $y=0.8x+2$. Predict $y$ when $x=10$.
13.
The regression lines are $4x-5y+33=0$ and $20x-9y-107=0$. Find $\bar x,\bar y$.
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.
The regression line of $y$ on $x$ is $y=1.5x+4$ and $\bar x=6$. Find $\bar y$, then predict $y$ when $x=10$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $(\bar x,\bar y)$
  2. (B) $y$ on $x$
  3. (B) $13$
  4. (B) $(\bar x,\bar y)$
  5. (A) $y-\bar y=b_{yx}(x-\bar x)$
Section B — Short Answer (2 marks)
  1. $13$.
  2. $4$.
  3. $(\bar x,\bar y)$.
  4. The line of $x$ on $y$.
Section C — Short Answer (3 marks)
  1. $\bar x=1,\ \bar y=2$.
  2. $\bar y=7$.
  3. $10$.
  4. $\bar x=13,\ \bar y=17$.
Section D — Long Answer (5 marks)
  1. $\bar x=13,\ \bar y=17$.
  2. $\bar y=13$; predicted $y=19$.
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