Tag: simple moving average

Questions Related to simple moving average

The independent variable in a regression line is: 

statistics time series moving average and variation simple moving average

  1. Non-random variable

  2. Random variable

  3. Qualitative variable

  4. None of these

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Correct Option: A
Explanation:

A linear regression line has an equation of the form $Y=a+bX$


where $Y$ is called dependent variable or response.
$X$ is called independent variable or predictors or explanatory variable 
$a$ is the y-intercept and
$b$ is the slope of the line.

The independent variable is a non-random variable. The non-random variable don't admit a probability measure.

In regression analysis, if observed cost value is $50$ and predicted cost value is $7$ then disturbance term is

statistics time series moving average and variation simple moving average

  1. $53$

  2. $37$

  3. $43$

  4. None of these

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Correct Option: C
Explanation:

Given that observed value is $50$ and

predicted value is $7$
The disturbance term is $observed - predicted=50-7=43$

State true or false: The coefficient of correlation between two variables $x$ and $y$ is:

$r=\cfrac { { \sigma }^{ 2 }x+{ \sigma }^{ 2 }y-y }{ 2{ \sigma }_{ x }{ \sigma } _{ y } } $

statistics time series moving average and variation simple moving average

  1. True

  2. False

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Correct Option: A
Explanation:
Coefficient of correlation is to express the degree of linear relationship between the two variables.
The coefficient of correlation between two variables $x$ and $y$ is given by

$r=\dfrac{\sigma^2x+\sigma^2y-y}{2\sigma_{x}\sigma_{y}}$

where $\sigma_x$ is the standard deviation of $x$ and
$\sigma_y$ is the standard deviation of $y$

The sum of the difference between the actual values of $Y$ and its values obtained from the fitted regression line is always:

statistics time series moving average and variation simple moving average

  1. Zero

  2. Positive

  3. Negative

  4. Minimum

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Correct Option: A
Explanation:

Let the actual values be $y_1,y_2,...,y_n$

Let the values obtained from the fitted regression analysis be $\hat y_1,\hat y_2,...,\hat y_n$

Since, the values are obtained from the fitted regression line.
Therefore, the actual and obtained values are almost equal.
Therefore, $y_1=\hat y_1$, $y_2=\hat y_2$ , ... , $y_n=\hat y_n$

sum of the difference between the actual and obtained values is $(y_1-\hat y_1)+(y_2-\hat y_2)+...+(y_n-\hat y_n)=0$

If all the actual and estimated values of $Y$ are same on the regression line, the sum of squares of error will be:

statistics time series moving average and variation simple moving average

  1. Zero

  2. Minimum

  3. Maximum

  4. Unknown

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Correct Option: A
Explanation:

Let the actual values be $y_1,y_2,...,y_n$

Let the estimated values be $\hat y_1,\hat y_2,...,\hat y_n$

Error is $actual-estimated$

Given that actual and estimated values are equal.
Therefore, $y_1=\hat y_1$, $y_2=\hat y_2$ , ... , $y_n=\hat y_n$

sum of squares of error is $(y_1-\hat y_1)^2+(y_2-\hat y_2)^2+...+(y_n-\hat y_n)^2=0$

The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to.

statistics time series moving average and variation simple moving average

  1. $1$ only

  2. $1$ or $-1$

  3. $-1$ only

  4. $0$

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Correct Option: B
Explanation:
The two regression lines are perpendicular to each other.

When coefficient of correlation is perfectly positive or negative $r$ = The two regression lines coincide 
Therefore the answer will be $1$ or $-1$

Find the equation of $y$ on $x$ on the basis of the following data:

$x$ $5$ $2$ $1$ $4$ $3$
$y$ $5$ $8$ $4$ $2$ $10$
statistics time series moving average and variation simple moving average

  1. $y=-0.8x+7$

  2. $y=0.4x+7$

  3. $y=-0.4x+7$

  4. $y=-0.4x-7$

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Correct Option: C
Explanation:
 $x$  $y$  $xy$  $x^2$
 5  5  25  25
 2  8  16  4
 1  4  4  1
 4  2  8  16
 3  10  30  9
 $\sum x=15$  $\sum y=29$  $\sum xy=83$  $\sum x^2=55$

The linear equation be y=a+bx

$n$ is the number of observations
$n=5$
where $a=\dfrac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}$
$\implies a=\dfrac{(29)(55)-(15)(83)}{5(55)-(15)^2}=\dfrac{350}{50}=7$
and $b=\dfrac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$
$\implies b=\dfrac{(5)(83)-(15)(29)}{5(55)-(15)^2}=\dfrac{-20}{50}=-0.4$
Therefore, $y=-0.4x+7$

Which of the following statements is/are correct in respect of regression coefficients?
$1.$ It measures the degree of linear relationship between two variables.
$2.$ It gives the value by which one variable changes for a unit change in the other variable.
Select the correct answer using the code given below.

statistics time series moving average and variation simple moving average

  1. $1$ only

  2. $2$ only

  3. Both $1$ and $2$

  4. Neither $1$ nor $2$

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Correct Option: A
Explanation:

When the regression line is linear $(y = ax + b)$ the regression coefficient is the constant $(a)$ that represents the rate of change of one variable $(y)$ as a function of changes in the other $(x)$ i.e. it is the slope of the regression line. Hence, it measures relationship between 2 variables but does not always account for exact change in value of 1 variable due to unit change in another variable due to non-zero value of $(b)$.

For 10 observations on price (x) and supply (y), the following data was obtained: $\sum x = 130, \sum y = 220, \sum x^2 = 2288, \sum y^2 = 5506$ and $\sum xy = 3467$. 
What is the line of regression of y on x?

statistics time series moving average and variation simple moving average

  1. $y = 0.91 x + 8.74$

  2. $y = 1.02x + 8.74$

  3. $y = 1.02 x - 7.02$

  4. $y = 0.91 x - 7.02$

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Correct Option: B
Explanation:
Line of regression of $y$ on $x$ is : $y - \overline{y} = b_{yx} (x - \overline{x})$ where $\overline{y}$ and $\overline{x}$ are mean values.
$\therefore \overline{y}=22, \overline{x}=13$ as $n=10$

Also, $b_{yx}=r\dfrac{\sigma_y}{\sigma_x}$

$\therefore r= \dfrac{n\sum-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}=0.962$

$\sigma_y=8.2$ and $\sigma_x=7.73$

$\therefore b_{yx}=1.02$

$\therefore y=1.02x+8.74$ is the required line of regression.

For two variables $x$ and $y$ ,the following data are given as
$\Sigma x=125,\Sigma y=100, \Sigma x^2=1650,\Sigma y^2=1500,\Sigma xy=50,n=25$.Find the value of $x$ when $y=5$

statistics time series moving average and variation simple moving average

  1. $5.231$

  2. $4.591$

  3. $6.564$

  4. $8.231$

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Correct Option: B