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Complete the following activity to find, the equation of line of regression of Y on X and X on Y for the following data:
Given:`n=8,sum(x_i-barx)^2=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`
Solution:
Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`
∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=square`
∴ `b_(xy)=(sum(x_i-barx)(y_i-bary))/(sum(y_i-bary)^2)=square`
∴ regression equation of Y on :
`y-bary=b_(yx)(x-barx)` `y-bary=square(x-barx)`
`x-barx=b_(xy)(y-bary)` `x-barx=square(y-bary)`
Concept: undefined >> undefined
Following table gives the number of road accidents (in thousands) due to overspeeding in Maharashtra for 9 years. Complete the following activity to find the trend by the method of least squares.
| Year | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 |
| Number of accidents | 39 | 18 | 21 | 28 | 27 | 27 | 23 | 25 | 22 |
Solution:
We take origin to 18, we get, the number of accidents as follows:
| Year | Number of accidents xt | t | u = t - 5 | u2 | u.xt |
| 2008 | 21 | 1 | -4 | 16 | -84 |
| 2009 | 0 | 2 | -3 | 9 | 0 |
| 2010 | 3 | 3 | -2 | 4 | -6 |
| 2011 | 10 | 4 | -1 | 1 | -10 |
| 2012 | 9 | 5 | 0 | 0 | 0 |
| 2013 | 9 | 6 | 1 | 1 | 9 |
| 2014 | 5 | 7 | 2 | 4 | 10 |
| 2015 | 7 | 8 | 3 | 9 | 21 |
| 2016 | 4 | 9 | 4 | 16 | 16 |
| `sumx_t=68` | - | `sumu=0` | `sumu^2=60` | `square` |
The equation of trend is xt =a'+ b'u.
The normal equations are,
`sumx_t=na^'+b^'sumu ...(1)`
`sumux_t=a^'sumu+b^'sumu^2 ...(2)`
Here, n = 9, `sumx_t=68,sumu=0,sumu^2=60,sumux_t=-44`
Putting these values in normal equations, we get
68 = 9a' + b'(0) ...(3)
∴ a' = `square`
-44 = a'(0) + b'(60) ...(4)
∴ b' = `square`
The equation of trend line is given by
xt = `square`
Concept: undefined >> undefined
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Find `dy/dx` if, x = e3t, y = `e^((4t+5))`
Concept: undefined >> undefined
Find `dy/dx` if, x = `e^(3t)`, y = `e^(4t+5)`
Concept: undefined >> undefined
Find `dy/dx if, x = e^(3t),y=e^((4t+5))`
Concept: undefined >> undefined
Find `dy/dx` if,
`x = e ^(3^t), y = e^((4t + 5))`
Concept: undefined >> undefined
Find `dy/dx` if, `x=e^(3t), y=e^((4t+5))`
Concept: undefined >> undefined
Find `dy/dx if,x = e^(3^T), y = e^((4t + 5)`
Concept: undefined >> undefined
Find `dy/dx` if x= `e^(3t)`, y =`e^((4t+5))`
Concept: undefined >> undefined
Find `dy/dx` if, `x = e^(3t), y = e^((4t + 5))`
Concept: undefined >> undefined
Find `dy/dx if, x= e^(3t)"," y = e^((4t+5))`
Concept: undefined >> undefined
Find `dy/dx` if, x = `e^(3t)`, y = `e^((4t + 5))`.
Concept: undefined >> undefined
Express the truth of each of the following statements by Venn diagram:
(a) Some hardworking students are obedient.
(b) No circles are polygons.
(c) All teachers are scholars and scholars are teachers.
Concept: undefined >> undefined
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
Concept: undefined >> undefined
If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`
Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`
Concept: undefined >> undefined
Draw a Venn diagram for the truth of the following statement :
All rational number are real numbers.
Concept: undefined >> undefined
Draw Venn diagram for the truth of the following statements :
Some rectangles are squares.
Concept: undefined >> undefined
Express the truth of each of the following statements using Venn diagrams:
(a) No circles are polygons
(b) Some quadratic equations have equal roots
Concept: undefined >> undefined
If x7 . y9 = (x + y)16 then show that `"dy"/"dx" = "y"/"x"`
Concept: undefined >> undefined
Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .
Concept: undefined >> undefined
