Correlation and Linear Regression - Probability and Statistics - Engineering Sciences Previous Year Questions

1

2007 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2007

The equation of the straight line of best fit using the following data by the principle of least square is

x	1	2	3	4	5
y	14	13	9	5	2

A

\(y = 18 - 3x \)

B

\(y = 18.1 - 3.1x \)

C

\(y = 18.2 - 3.2x \)

D

\(y = 18.3 - 3.3x \)

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2

2008 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2008

The two lines of regression of the variables \( x \) and \( y \) are \( 4x + 2.4y = 20 \) and \( 1.6x + 4y = 12 \). The coefficient of correlation between \( x \) and \( y \) is

A

0.49

B

-0.49

C

0.35

D

-0.35

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3

2008 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2008

The following table gives a function \(f(x)\) vs \(x\).

\(x\)	0	1	2	3	4
\(f(x)\)	1.0	3.7	6.5	9.3	12.1

The best fit of a straight line for the above data points, using a least square error method is

A

\(2.75x + 0.55\)

B

\(2.80x + 0.80\)

C

\(3.10x + 0.85\)

D

\(2.78x + 0.96\)

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4

2016 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2016

The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is ______.

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5

2017 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2017

The points in the graph below represent the halts of a lift for durations of 1 minute, over a period of 1 hour.
Which of the following statements are correct?
i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period
ii. The elevator stays on the fourth floor for the longest duration over the one hour period

A

Only i

B

Only ii

C

Both i and ii

D

Neither i nor ii

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6

2019 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2019

Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?

A

16.24

B

23.97

C

25.86

D

38.74

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7

2020 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2020

The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 - 2018 is ____.

A

15 : 17

B

16 : 17

C

17 : 15

D

17 : 16

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8

2024 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2024

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023.

The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from 2007 to 2023, what is the percentage increase in the share of the renewable sources of electricity generation over this period?

A

25%

B

50%

C

77.5%

D

62.5%

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9

2026 · Engineering Sciences · Probability and Statistics · Correlation and Linear Regression

Engineering Sciences (XE) 2026

Which of the following statements is/are true?

A

\(Y = 1 + 1.8X \) and \(X = 1 - 0.5Y \) are estimated as lines of regression of \(Y \) on \(X \) and \(X \) on \(Y \), respectively.

B

\(Y = 1 + 1.3X \) and \(X = 2 + 1.1Y \) are estimated as lines of regression of \(Y \) on \(X \) and \(X \) on \(Y \), respectively.

C

\(Y = 1 + 1.6X \) and \(X = 3 + 0.5Y \) are estimated as lines of regression of \(Y \) on \(X \) and \(X \) on \(Y \), respectively.

D

\(Y = 1 + X \) and \(X = Y \) are estimated as lines of regression of \(Y \) on \(X \) and \(X \) on \(Y \), respectively, and the correlation between \(X \) and \(Y \) is \(\pm 1 \).

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