Bissoy.com
Doctors Medicines MCQs Q&A

Study the following production data of a sugar factory. Year 2001 2002 2003 2004 2005 2006 2007 Production (‘000 tonnes) (y) 76 87 95 81 91 96 90   What is the estimate of the production for 2008 using straight-line trend - with the origin at the year 2001 - by the least-squares method \((\sum x= 0, \sum x^2 = 28, \sum xy = 56) ?\)

Study the following production data of a sugar factory. Year 2001 2002 2003 2004 2005 2006 2007 Production (‘000 tonnes) (y) 76 87 95 81 91 96 90   What is the estimate of the production for 2008 using straight-line trend - with the origin at the year 2001 - by the least-squares method \((\sum x= 0, \sum x^2 = 28, \sum xy = 56) ?\) Correct Answer 102

Given

∑x = 0

∑x2 = 28

∑xy = 56

Formula

a = ∑y/n

b = ∑xy/∑x2

Explanation

Year

y

2001

76

2002

87

2003

95

2004

81

2005

91

2006

96

2007

90

N = 7

∑y = 616

Y = a + bx

⇒ a = 616/7

⇒ a = 88

⇒ b = 56/28

⇒ b = 2

Y = 88 + 2x

⇒ X = 2008 – 2001 = 7

Y = 88 + 2 × 7

∴ estimate of the production for 2008 is 102

Related Questions

The table shows the different expenditures of a firm in different years. In which year was the total expenditure the highest? Year Particulars (in Rs) Purchases wages Rent Interest Delivery 2016 1,00,000 1,40,000 1,60,000 80,000 80,000 2017 1,20,000 1,54,000 1,36,000 1,70,000 90,000 2018 1,60,000 1,20,000 1,44,000 1,46,000 1,20,000 2019 1,76,000 1,44,000 1,80,000 90,000 1,10,000 2020 2,00,000 1,60,000 1,12,000 80,00 1,30,000
On 1st January, 2004, 'A' took a mine on lease for 10 years. The rate of profession fee is 50 paise per tonne and the minimum fare is Rs. 8,000 per annum. Short working amount has the right to be recovered till 31st December, 2008. Production was as follows-
2004 ⇔ 3,000 ton, 2005 ⇔ 10,000 ton, 2006 ⇔ 20,000 ton, 2007 ⇔ 28,000 ton, 2008 ⇔ 14,200 ton.
The amount to be given to the landlord for the year 2006 is
Following table shows the production of sugar in thousand tons by three sugar mills A, B, and C during the period 2001 to 2005. Year Production in Thousand Tons A B C 2001 24 18 13 2002 27 20 15 2003 29 22 19 2004 29 25 21 2005 32 28 22   The smallest change in the total production of sugar by A and C together occurred in the year:
The following table gives the sales of Drinks manufactured by a company over the years. Study the table below and answer the questions that follow: Number of different types of Drinks sold by a company over the year(in thousands) Year Pepsi Miranda Fanta Coke Sprite Total 2002 75 144 114 102 108 543 2003 90 126 102 84 126 528 2004 96 114 75 105 135 525 2005 105 90 150 90 75 510 2006 90 75 135 75 90 465 2007 105 60 165 45 120 495 2008 115 85 160 100 145 605 What is the difference in the number of coke drink sold in the 2003 and 2007?
The following table gives the sales of Drinks manufactured by a company over the years. Study the table below and answer the questions that follow: Number of different types of Drinks sold by a company over the year(in thousands) Year Pepsi Miranda Fanta Coke Sprite Total 2002 75 144 114 102 108 543 2003 90 126 102 84 126 528 2004 96 114 75 105 135 525 2005 105 90 150 90 75 510 2006 90 75 135 75 90 465 2007 105 60 165 45 120 495 2008 115 85 160 100 145 605 In the case of which drink there was continuous decrease in sales from 2002 to 2007?
The following table gives the sales of Drinks manufactured by a company over the years. Study the table below and answer the questions that follow: Number of different types of Drinks sold by a company over the year(in thousands) Year Pepsi Miranda Fanta Coke Sprite Total 2002 75 144 114 102 108 543 2003 90 126 102 84 126 528 2004 96 114 75 105 135 525 2005 105 90 150 90 75 510 2006 90 75 135 75 90 465 2007 105 60 165 45 120 495 2008 115 85 160 100 145 605 what was the approximate percentage increase in the sales of sprite in 2008 compared to that in 2002?
The following table presents the number of candidates trained by a training centre over 6 years (2001 to 2006). Year Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 2001 75 144 114 102 108 2002 90 126 102 84 126 2003 96 114 75 105 135 2004 105 90 150 90 75 2005 90 75 135 75 90 2006 105 60 165 45 120 The number of candidates trained in Batch 2 in 2001 was what percentage more than the number of candidates trained in Batch 5 in 2005?
In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data.
A company produced a new energy drink of three different flavours - P, Q and R - for athletes. The production of the three flavours over a period of six years from 2001 to 2006 has been expressed in the bar graph shown below. Study the graph and answer the question that follows.    What is the difference between the average production of bottles of flavour Q in 2004, 2005 and 2006 and the average production of flavour P in 2001, 2002 and 2003?
The given bar graph represents data of the production of paper (in ten lakh tonnes) by three different companies X, Y and Z during the years 2008 to 2012. The x-axis shows the 'years' and the y-axis represents the 'production of paper (ten lakh tonnes)'. (Note: The data shown is only for mathematical exercise. They do not represent actual figures.)  The total production of Company Y during 2008 and 2009 and Company X for 2011 and 2012 taken together is p% (p is correct to the nearest integer) more than the total production of Company Z during 2010, 2011 and 2012. The total production of Company Z during 2008 and 2009 taken together is q% (q is correct to the nearest integer) less than the total production of Company X during 2008, 2009 and 2012 and Company Y during 2010 and 2011 all together.  What is the positive difference between p and q ?