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Assuming that the data satisfy the requirements of errors that are independent and identically distributed, the regression model that is often fitted takes the form of

fitted(y) = b0 + b1*x

(This browser is so useless that it does not properly support characters from other althabets and not even subscripts!)

If there is a linear relationship between the independent variable,x , and the dependent variable, y, then b1 must be non-zero. You would therefore test the null hypothesis that b1 is equal to 0 against the alternative hypothesis, which may be that

* b1 is not 0, or

* b1 is greater than 0, or

* b1 is less than 0.

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Q: Why shall we test H0 β1 0 for a simple linear regression?
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