Question

If we performed 20 different linear regressions at the 0.10 level, how many of these would we expect to show significance by chance?

0

2

5

10

20

Answer 1

Answer is 2

Note :

By testing significance in linear regression we mean testing whether the slope coefficient is different from zero .

The equation of line of regression is

The null hypothesis is

Given ,Significance level = 0.10

It is the probability of type I error ( rejecting H0 when it is true)

That is probability of getting significant result (that is getting significantly different from zero ) given null hypothesis is true ( that is =0 is true) is 0.10

Can also be stated as :Under the cirumstance of true null hypothesis , we expect to get 10% results significant by chance .

Thus out of 20 tests , 20*0.10 =2 tests can be expected to give significant resultby chance .