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Two-tailed t-tests are used in regressions to test for effects in either direction.
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Reference material confirms that two-tailed significance tests evaluate parameters for differences or effects in either direction, and statistical literature demonstrates their application in regression analyses to test coefficient significance.

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In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of sco In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is accepted over the null hypothesis. Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often "tail off" toward zero as in the normal distribution, colored in yellow, or "bell curve", pictured on the right and colored in green.
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rails:sufficiency:supported:for=2+0p:against=0+0p | v55:sufficiency

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You can find this value to the right of the standard error of the coefficient estimate. The standard error of the coefficient for b1 is Sb1 in the formula. To reach a conclusion we compare this test statistic with the critical value of the student’s t at degrees of freedom n-3-1 =29, and alpha = 0.025 (5% significance level for a two-tailed test). Our t stat for b1 is approximately 5.90 which is greater than 1.96 (the critical value we looked up in the t-table), so we cannot accept our null hypotheses of no effect. We conclude that Price has a significant effect because the calculated t value is in the tail. We conduct the same test for b2 and b3. For each variable, we find that we cannot accept the null hypothesis of no relationship because the calculated t-statistics are in the tail for each case, that is, greater than the critical value. All variables in this regression have been determined to have a significant effect on the demand for roses. These tests tell us whether or not an individual coefficient is significantly different from zero, but does not address the overall quality of the model.
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  1. One- and two-tailed testsreferenceno side taken
  2. OpenStax Introductory Business Statistics: 13.7 How to Use Microsoft Excel® for Regression Analysisreferenceno side taken
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