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Question: In a bivariate data \(\sum_{}^{}{x = 30},\sum_{}^{}{y = 400}\), \(\sum_{}^{}{x^{2} = 196},\sum_{}^{}...

In a bivariate data ∑x=30,∑y=400\sum_{}^{}{x = 30},\sum_{}^{}{y = 400}, ∑x2=196,∑xy=850\sum_{}^{}{x^{2} = 196},\sum_{}^{}{xy = 850} and n=10n = 10.The regression coefficient of y on x is

A

– 3.1

B

– 3.2

C

– 3.3

D

– 3.4

Answer

– 3.3

Explanation

Solution

Cov(x,y)=1n∑xy−1n2∑x.∑yCov(x,y) = \frac{1}{n}\sum xy - \frac{1}{n^{2}}\sum x.\sum y = 110(850)−1100(30)(400)\frac{1}{10}(850) - \frac{1}{100}(30)(400) = −35- 35

Var(x)=σx2=1n∑x2−(∑xn)2Var(x) = \sigma_{x}^{2} = \frac{1}{n}\sum x^{2} - \left( \frac{\sum x}{n} \right)^{2}= 19610−(3010)2\frac{196}{10} - \left( \frac{30}{10} \right)^{2} = 10.6

byx=Cov(x,y)Var(x)=−3510.6b_{yx} = \frac{Cov(x,y)}{Var(x)} = \frac{- 35}{10.6}= – 3.3.