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ECON301_Handout_06_1213_02

ˆ 2101 2101 t since 1 0025 ˆ tt we reject the null

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ˆ 2.101 2.101 t . Since, 1 0.025 ˆ tt , we reject the null hypothesis and conclude that 1 is statistically significant from zero at 0.05 level of significance. Example 2 Suppose that we have the ten pairs of observations on X (price) and Y (quantity supplied) shown in table below. Obs. Y (Quantity) X (Price) 1 69 9 2 76 12 3 52 6 4 56 10 5 57 9 6 77 10 7 58 7 8 55 8 9 67 12 10 53 6 11 72 11 12 64 8 Using the formulas for intercept and slope terms, we got the following estimated supply function: ˆ 33.75 3.25 YX 
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ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 14 For the estimation we have used the OLS formulas in mean deviation form: 1 1 2 1 156 ˆ 3.25 48 T tt t T t t xy x and, 01 ˆˆ 63 (3.25)(9) 33.75 YX    Obs. Y (Quantity) X (Price) y x xy x 2 1 69 9 6 0 0 0 2 76 12 13 3 39 9 3 52 6 -11 -3 33 9 4 56 10 -7 1 -7 1 5 57 9 -6 0 0 0 6 77 10 14 1 14 1 7 58 7 -5 -2 10 4 8 55 8 -8 -1 8 1 9 67 12 4 3 12 9 10 53 6 -10 -3 30 9 11 72 11 9 2 18 4 12 64 8 1 -1 -1 1 Y = 63 X = 9 xy=156 x 2 =48 0 ˆ 33.75 1 ˆ 3.25 Show that the standard errors are: 00 2 2 0 2 ˆ (or ( )or ) 8.28 t t X s se Tx  11 2 1 2 1 ˆ (or ( ) 0.89 t s se x
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ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 15 The t values for the two parameter estimates are 0 0 ˆ 0 ˆ 33.75 4.08 8.28 ˆ () t se 1 1 ˆ 1 ˆ 3.25 3.65 0.89 ˆ t se Since 0 0.025 ˆ 4.08 tt and 1 0.025 ˆ 3.65 , both estimates are statistically significant at 0.05 level of significance. ii. One Sided (or One Tailed) t Test The most common use of the one-sided t -test is to determine whether a regression coefficient has the sign or value range predicted by economic theory. Possible one sided hypotheses around zero are: 01 1 :0 A H H and 1 A H H
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ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 16 Possible one-sided hypotheses based on hypothesized values other than zero are: * 0 1 1 * 11 : : A H H  and * 0 1 1 * : : A H H a. Steps of One-Sided Individual Test Step 1. 00 : i H versus 0 : i A H Step 2. Construct the t-statistic ˆ ˆ ˆ () i i i t se , where ˆ 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 Tk t  such that the area to the right of it is equal to the level of significance .
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ˆ 2101 2101 t Since 1 0025 ˆ tt we reject the null...

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