ECON301_Handout_06_1213_02

# I is the estimate and ˆ i se is its standard error 5

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i is the estimate and ˆ ( ) i se is its standard error 5 . If 0 0 , this t-value reduces to the ratio of regression coefficient to its standard error. Under 0 H , it has a t -distribution with T-k-1 degrees of freedom, where T is total number of observations, k is the number of slope terms and 1 is for the intercept term in the regression. Step 3. Look up in the t -table the entry corresponding to T-k-1 degrees of freedom and find the critical point * 1 ( ) T k t   such that the area to the right of it is equal to the level of significance ( ) . 5 It can be denoted by ˆ ˆ i or ˆ i s instead of ˆ ( ) i se .

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ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 17 Step 4. Reject the null hypothesis if * ˆ 1 ( ) i T k t t   . If the alternative had been 0 : i A H , 0 H would have been rejected if * ˆ 1 ( ) i T k t t     . Equivalently, for either alternative, reject 0 H if * ˆ 1 ( ) i T k t t   . Using p -value approach, reject 0 H if the p -value is less than the level of significance. t Test: Decision Rules for all cases Type of hypothesis H 0 : the null hypothesis H 1 : the alternative hypothesis Decision rule: reject H 0 if Two-tail * i i * i i /2, df t t Right-tail * i i * i i , df t t Left-tail * i i * i i , df t t  Notes: * i is the hypothesized numerical value of i . | t | means the absolute value of t . t or /2 t means the critical t value at the α or α/2 level of significance. df : degrees of freedom, (T − 2) for the two -variable model (including intercept), (T k 1) for the k independent variable model (including intercept).
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