Tag: time series

Quizzes (7) Questions (24)

Questions Related to time series

Multiple choice statistics time series moving average and variation simple moving average

What would be the estimated sale on the advertisement expenditure of Rs $15$ lakhs,on the basis of following data obtained from the company?.The coefficient of correlation is $0.8$.

Advertising expenditure(in Rs.lakhs) $x$ Sale (in Rs lakhs) $y$
Mean $20$ $90$
standard Deviation $5$ $12$
  1. Rs $105$ lakhs
  2. Rs$106$ lakhs
  3. Rs $110$ lakhs
  4. Rs $120$ lakhs
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\bar x=20$, $\bar y=90$, $\sigma_x=5$, $\sigma_y=12$ and $r=0.8$
Regression line of y on x will be $y-\bar y=r\dfrac{\sigma_y}{\sigma_x}(x-\bar x)$
Subsitute all the abpve value in an equation of regression line, we get
$y-90=\dfrac{0.8\times 12}{5}(x-20)$
$y-90=1.92(x-20)$
$y=1.92x+90-38.4$
Now, Subsitute the value of x=15, we get
$y=1.92\times 15+51.6=80.4$

Multiple choice statistics time series moving average and variation simple moving average

Find the equation of $y$ on $x$ for the following data

$x$ $8$ $6$ $4$ $7$ $5$
$y$ $9$ $8$ $5$ $6$ $2$
  1. $y=2x -1.2$
  2. $y=1.2x +1.2$
  3. $y=1.2x -1.2$
  4. $y=1.2x -2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
 $x$  $y$  $x^2$  $x\times y$
 $8$  $9$  $64$  $72$
 $6$  $8$  $36$  $48$
 $4$  $5$  $16$  $20$
 $7$  $6$  $49$  $42$
 $5$  $2$  $25$  $10$

$\sum x=30$
$\sum y=30$
$\sum x^2=190$
$\sum x\times y=192$
So, $\bar x=\dfrac{\sum x}{n}=\dfrac{30}{5}=6$
$\bar y=\dfrac{\sum y}{n}=\dfrac{30}{5}=6$
$b_{yx}=\dfrac{\sum xy-\dfrac{\sum x \times \sum y}{n}}{\sum x^2-\dfrac{(\sum
x)^2}{n}}=\dfrac{192-180}{190-180}=\dfrac{12}{10}=1.2$
Regression line of y on x will be $y-\bar y=b_{yx}(x-\bar x)$
$y-6=1.2(x-6)$
$y=1.2x-7.2+6$
$y=1.2x-1.2$

Multiple choice statistics time series moving average and variation simple moving average

For the variables $x$ and $y$, the regression equations are given as $7x-3y-18=0$ and $4x-y-11=0$. Find the arithmetic means of $x$ and $y$ respectively.

  1. $3$ and $1$
  2. $1$ and $3$
  3. $2$ and $4$
  4. $4$ and $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the two lines of regression interest at the point $(\bar{X}, \bar{Y} )$


Replace $x$ and $y$ by $\bar{X}$ and $\bar{Y}$ respectively in the given regression equations.

We get,
$7\bar{X}- 3\bar{Y} - 18 = 0$ and $4\bar{X}-\bar{Y} - 11 = 0$ 


Solving these equations, we get $\bar{X} = 3$ and $\bar{Y} = 1$ 

Thus the arithmetic mean of $x$ and $y$ is given by $3$ and $1$ respectively.

Multiple choice statistics time series moving average and variation simple moving average

The two lines of regression are $x+2y-5=0$ and $x+3y-8=0$. The coefficient of correlation between $x$ and $y$ is 

  1. $-0.72$
  2. $0.72$
  3. $-0.82$
  4. $0.82$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given two lines $x+2y-5=0, x+3y-8=0$.

Consider $x+2y-5=0$
$\Rightarrow x=-2y+5$
$\Rightarrow r_1=-2$
Consider $x+3y-8=0$
$\Rightarrow y=-\dfrac{1}{3}x+\dfrac{8}{3}$
$\Rightarrow r_2=-\dfrac{1}{3}$
We know that $r^2=r_1 \times r_2$
$\Rightarrow r^2=-2 \times -\dfrac{1}{3}$
$\Rightarrow r^2=\dfrac{2}{3}$
$\Rightarrow r=\pm \sqrt{\dfrac{2}{3}}$
We know that, If both regression coefficients are negative, $r$ would be negative.
$\Rightarrow r=-\sqrt{\dfrac{2}{3}}=-0.82$