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Statistics MCQ

PART 1 : LINEAR REGRASSION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 17 questions.

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17 questions · timed · auto-graded

MCQ 11 Mark
If $r=0.6$, how much percent of the total variations in the dependent variable can not be explained by the regression model ?
  • A
    $40$
  • B
    $36$
  • ✓
    $64$
  • D
    $16$
Answer
Correct option: C.
$64$
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MCQ 21 Mark
What will be the value of correlation coefficient if the coefficient of determination between two variables is $0.49$ ?
  • A
    $-0.49$
  • B
    $+0.49$
  • ✓
    $\pm 0.7$
  • D
    $+0.51$
Answer
Correct option: C.
$\pm 0.7$
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MCQ 31 Mark
What will be the value of $b_{y x}$ if $v=15(y-75), u=6(x-50)$ and $b_{v u}=3.5$ ?
  • ✓
    $1.4$
  • B
    $0.03$
  • C
    $8.75$
  • D
    $315$
Answer
Correct option: A.
$1.4$
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MCQ 41 Mark
If $u=\left(\frac{x-400}{100}\right), v=\left(\frac{y-25}{5}\right)$ and $b_{y x}=2.8$ then what will be the value of $b_{v u} ?$
  • A
    $2.8$
  • B
    $0.14$
  • C
    $28$
  • ✓
    $56$
Answer
Correct option: D.
$56$
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MCQ 51 Mark
If $R^2=r^2=1$ then what type of correlation is obtained between the variables $X$ and $Y$ ?
  • A
    partial positive linear correlation
  • B
    partial negative linear correlation
  • ✓
    perfect linear correlation
  • D
    lack of linear correlation
Answer
Correct option: C.
perfect linear correlation
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MCQ 61 Mark
What will be the value $b_{y x}$ if the regression line of $Y$ on $X$ is $5 x-9 y+108=0$ ?
  • A
    $-\frac{5}{9}$
  • ✓
    $\frac{5}{9}$
  • C
    $-\frac{9}{5}$
  • D
    $\frac{9}{5}$
Answer
Correct option: B.
$\frac{5}{9}$
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MCQ 71 Mark
If the regression line of $Y$ on $X$ is $\hat{y}=35-0.2 x$, what is the estimated value of $Y$ if $X=50$ ?
  • A
    $-65$
  • B
    $-25$
  • C
    $65$
  • ✓
    $25$
Answer
Correct option: D.
$25$
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MCQ 81 Mark
If the regression line of $Y$ on $X$ is $\hat{y}=20+4.5 x$, what is the estimated value of $Y$ for $X=35$ ?
  • A
    $157.5$
  • B
    $24.5$
  • ✓
    $177.5$
  • D
    $59.5$
Answer
Correct option: C.
$177.5$
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MCQ 91 Mark
While obtaining the regression line, what will be the sum of the squares of errors?
  • ✓
    minimum
  • B
    maximum
  • C
    zero
  • D
    one
Answer
Correct option: A.
minimum
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MCQ 101 Mark
If $b>0$, what will be the change in the estimated value of dependent variable $Y$ if the value of independent variable $X$ increases?
  • ✓
    increases
  • B
    decreases
  • C
    not changed
  • D
    can't say anything for the change While obtaining the regression line, what will be the sum of the squares of errors?
Answer
Correct option: A.
increases
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MCQ 111 Mark
Regression line always passes through which point?
  • ✓
    $(\bar{x}, \bar{y})$
  • B
    $(\bar{x}, b)$
  • C
    $(a, b)$
  • D
    $(a, \bar{y})$
Answer
Correct option: A.
$(\bar{x}, \bar{y})$
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MCQ 131 Mark
What is ' $a$ ' in the regression line $\hat{y}=a+b x$ ?
  • A
    Regressions coefficient
  • ✓
    Intercept
  • C
    Disturbance variable
  • D
    Correlation coefficient
Answer
Correct option: B.
Intercept
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MCQ 141 Mark
Which method is subjective for the fitting of the regression line ?
  • ✓
    Scatter diagram method
  • B
    Least square method
  • C
    Karl Pearson's method
  • D
    Spearman's method
Answer
Correct option: A.
Scatter diagram method
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MCQ 151 Mark
Which regression line is used if the sale of an item depends on its advertisement cost ?
  • ✓
    Regression line of sale of an item on advertisement cost
  • B
    Regression line of advertisement cost on sale of an item
  • C
    Regression line of sale of an item on sale of item
  • D
    Regression line of advertisement cost on advertisement cost
Answer
Correct option: A.
Regression line of sale of an item on advertisement cost
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MCQ 161 Mark
In the regression model $Y=\alpha+\beta x+u$, what type of the variable is $'u'\ ?$
  • A
    Independent variable
  • B
    Dependent variable
  • ✓
    Disturbance variable
  • D
    Causal variable
Answer
Correct option: C.
Disturbance variable
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MCQ 171 Mark
During the study of human inheritance, which statistician was the first to use the term 'regression'?
  • A
    Karl Pearson
  • B
    Spearman
  • ✓
    Sir Francis Galton
  • D
    C. F. Gauss
Answer
Correct option: C.
Sir Francis Galton
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MCQ - Statistics STD 12 Commerce Questions - Vidyadip