Lakshya Education MCQs

Question: The quantity of goods produced and costs incurred by a firm are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

Quantity producedTotal cost1012020230303154042550510
Options:
A.0.85
B.0.93
C.0.97
D.0.99
Answer: Option D
: D

XiYiX2iY2iXiYi1012010014400120020230400529004600303159009922594504042516001806251700050510250026010025500=150=1600=5500=607250=57750

r=Nni=1(XiYi)(ni=1Xi)(ni=1Yi)Nni=1X2i(ni=1Xi)2Nni=1Y2i(ni=1Yi)2=4875070.71×690.11=0.999

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More Questions on This Topic :

Question 1. Use the line of best fit to predict the approximate value of y when x is equal to 10.

 

  1.    20
  2.    30
  3.    40
  4.    50
Answer: Option B
: B

Draw a line parallel to the y-axis through x=10 to intersect the line of best fit. Through this point, draw a line parallel to the x-axis to intersect the y-axis. It can be seen that this line cuts y-axis near 30. Hence the approximate value of y corresponding to x=10 is 30.
Question 2. The ages and weights of 5 children are given below. Calculate covariance.

Age, X)Weight, Y720925113613411548
  1.    14.6
  2.    22.7
  3.    28.8
  4.    36
Answer: Option C
: C

XYX¯XY¯Y(X¯X)(Y¯Y)720414569252918113602013412714154841456=144 ¯X=XN=555=11
¯Y=YN=1705=34 Cov(X,Y)=(X¯X)(Y¯Y)N=1445=28.8
Question 3. Spearman's rank coefficient is used to understand the correlation between variables which can be clearly quantified. State true or false.
  1.    True
  2.    False
  3.    0.965
  4.    0.982
Answer: Option B
: B

False. Spearman’s Rank coefficient helps us understand the correlation between the variables which can’t be very meaningful and predominantly subjective. It is generally used to find the correlationin caseof qualitative variables.
Question 4. Spearman's rank coefficient can be used to answer the question:



Does the number of symptoms a patient has indicate a higher severity of illness?
  1.    False
  2.    True
  3.    0.97
  4.    0.99
Answer: Option B
: B

Spearman's rank coefficient helps to understand the type of correlation by looking at non-linear ranked data. Hence this question can be answered using the same.
Question 5. Calculate the correlation coefficient for the following data.



XY243649510611713817
  1.    0.878
  2.    0.925
  3.    0.965
  4.    0.982
Answer: Option D
: D

xyx¯x(x¯x)2(y¯y)(y¯y)2(x¯x)(y¯y)2439636183624416849111115100000061111111713243968173974921=28=112=55 ¯x=xn=357=5
¯y=yn=707=10 r=ni=1(xi¯x)(yi¯y)ni=1(xi¯x)2ni=1(yi¯y)2=5528×112=5556=0.982

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