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Answer these questions fast ​-example-1
User JAnton
by
7.2k points

1 Answer

2 votes

Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

¯

y

=

b

y

x

(

x

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

x

y

1

n

x

y

x

2

1

n

(

x

)

2

=

1944

1

5

×

98

×

69

2580

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

¯

y

=

b

y

x

(

x

¯

x

)

y

13.8

=

0.898

(

x

19.6

)

y

=

0.898

x

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

User Jdstaerk
by
8.1k points

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