1 Marks Each

Question 11 Mark

Will the regression co-efficient change if the values of both the variables are doubled with the help of transformation of scale ?

Answer

The regression co-efficient will not change if the values of both the variables are doubled.

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Question 21 Mark

What is the value of error if a sample point is on the fitted line ?

Answer

The value of error is zero $(0)$ if a sample point is one the fitted line.

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Question 31 Mark

The regression co-efficient is not independent of which transformation ?

Answer

The regression co-efficient is not independent from the change of scale.

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Question 41 Mark

The regression co-efficient is independent of which transformation ?

Answer

The regression co-efficient is independent from the change of origin.

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Question 51 Mark

Give the name of a method to obtain the best fitted regression line.

Answer

Method to obtain the best fitted regression line is 'least square method'.

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Question 61 Mark

What is an error in context with a regression line ?

Answer

The difference between the observed value $y$ of the variable $Y$ and the estimated value $ŷ$ of $y$ obtained by the regression model is called an error in context with a regression line. It is denoted by $‘e’.$ Thus, $e = y – ŷ.$

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Question 71 Mark

Define : Regression co-efficient.

Answer

The co-efficient of $b$ of $x$ in the linear regression model $y = a + bx$ is known as co-efficient of regression.
OR The approximate change in the value of dependent variable for a unit change in the value of independent variable.
b represents the appropriate increase or decrease in the value of $Y$ per one unit increase or decrease in the value of $X.$

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Question 81 Mark

If $Y = 5 – 3x$ is the relation between $Y$ and $X$ then what is the value of $r\ ?$

Answer

$y = 5 – 3x $
$\therefore b = – 3.$
Here the value of $r$ is $-1.$

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Question 91 Mark

If $Y$ and $X$ have the relation $y = a + bx,$ where $b > 0,$ then what is the value of $r\ ?$

Answer

$y = a + bx;$ where $b > 0,$ then the value of $r$ is $1.$

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Question 101 Mark

If $r=0.5, S_x=2 ; S_y=4$ what is the value of $b_{y x}$ ?

Answer

$
r=0.5, S_x=2, S_y=4
$
Now, $b_{y x}=r \cdot \frac{S_y}{ S _x} ;$ putting the values given.
$
\therefore b_{y x}=0.5 \times \frac{4}{2}=0.5 \times 2=1
$

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Question 111 Mark

Define : Linear Regression

Answer

The relation between two variables determined by an appropriate mathematical function which is represented by a straight line, then it is known as linear regression.

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Question 121 Mark

State the constants of linear regression model.

Answer

In the linear regression model.
$Y = a + \beta X + u , a$ and $\beta$ are constants.

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Question 131 Mark

In regression model how is the dependent variable $Y$ expressed?

Answer

In regression model the dependent variable $Y$ is expressed as a proper mathematical function of $X.$

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Question 141 Mark

What is explained variable?

Answer

Out of two variables, having cause-effect relationship, effect variable is called explained variable.

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Question 151 Mark

What is called explanatory variable?

Answer

Out of two variables having cause- effect relationship, the causal variable is called explanatory variable.

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Question 161 Mark

What is regression model?

Answer

A statistical model which describes the cause and effect relationship between two variables is called a regression model.

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Question 171 Mark

What is a model?

Answer

A set of one or more equations representing a relation or a problem is called a model.

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Question 181 Mark

During which type of study was the term regression first used by sir Francis Galton?

Answer

During the study of human inheritance the term regression was first used by Sir Francis Galton.

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Question 191 Mark

State the literal meaning of regression.

Answer

The literal meaning of regression is ‘to avert’ or ‘to return to average value’.

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Question 201 Mark

Will the regression coefficient change If the values of both the variables are doubled with the help of transformation of scale?

Answer

If the values of both the variable are doubled then the value of the regression coefficient will not change, because $C_x = \frac{1}{2}$ and $C_y = \frac{1}{2}$

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Question 211 Mark

Which statistician initiated the study of regression ?

Answer

English Statistician Sir Francis Galton initiated the study of regression.

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Question 221 Mark

Which variable is independent and which is dependent in cause and effect relationship ?

Answer

Out of two variables, variables which is the form of cause is said to be independent variable, while which is in the form of effect is said to be dependent variable.

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Question 231 Mark

What is regression ?

Answer

Regression is the relation between two variable determined by an appropriate mathematical function.

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Question 241 Mark

Which measure is useful to know the effect of one variable occured due to the effect of another variable ?

Answer

Regression co-efficient is useful measure to know the effect of one variable occured due to the effect of another variable.

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Question 251 Mark

State the linear regression model that represents the relation between two random variables $Y$ and $X.$

Answer

Ans: Linear regression model $y = \alpha + \beta x + u;$
Where, $\alpha $ and $\beta$ are constants and u is an error variable.

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Question 261 Mark

What is linear regression model ?

Answer

When the relation of linear correlation between two variables is represented by an equation, it is called the linear regression model.

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Question 271 Mark

What Is the assumption for the study of regression ?

Answer

Before study of regression, we have to assume that there is cause and effect relationship between two variables.

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Question 281 Mark

Will the regression coefficient change if the values of both the variables x and y are doubled with the help of transformation of scale ?

Answer

No, the regression coefficient $b_{yx}$ will not change because the scale factor for both $x$ and $y$ is the same (multiplied by 2), and $b_{vu} = b_{yx} \cdot \frac{C_x}{C_y}$. Since $C_x=2$ and $C_y=2$, the ratio is 1.

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Question 291 Mark

If $ r=0.5, S_{x}=2, S_{y}=4 $, what is the value of regression coefficient $ b_{yx} $ ?

Answer

$ b_{yx} = r \cdot \frac{S_{y}}{S_{x}} = 0.5 \cdot \frac{4}{2} = 0.5 \cdot 2 = 1 $

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