Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.] Standard Error t Stat p-value Coefficients Intercept 37.0151 12.6751 2.920 0.006 x1 0.9322 0.9250 1.008 0.320 a. Specify the hypotheses to determine if the slope differs from minus one. H0: ?1 ? -1; HA: ?1 < -1 H0: ?1 = -1; HA: ?1 ? -1 H0: ?1 ? -1; HA: ?1 > -1 b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic
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We want to test if the slope differs from -1. So, the hypotheses are: H0: β1 = -1 HA: β1 ≠ -1 Now, we need to calculate the test statistic. The test statistic for a hypothesis test about the slope in a simple linear regression is given by: t = (b1 - β1) / Show more…
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Consider the following regression results based on 20 observations. [You may find it useful to reference the t table.] Coefficients Standard Error t Stat p-value Intercept 33.6043 4.5468 7.391 0.000 x1 0.1001 0.1431 0.700 0.493 a-1. Choose the hypotheses to determine if the intercept differs from zero. H0: β0 = 0; HA: β0 ≠ 0 H0: β0 = 0; HA: β0 ≠ 0 H0: β0 = 0; HA: β0 ≠ 0 Construct the 95% confidence interval for the slope coefficient. (Negative values should be indicated by a minus sign. Round "tα/2,df" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval: ___________ to ___________
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The proportion of variability in Y that can be explained by the linear relationship to X 77.574 The test statistic for testing the hypotheses, 3.096 Ho B1 = 0 vs Ha : B1 = 0. 25.052 7.567 The standard error for the regression model: 1.131 The expected value of Y variable when * 6.689 7,668 The standard error value you would use t0 construct a confidence interval for the actual slope; 81 0.4355
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In a simple linear regression based on 32 observations, it is found that b1 = 7.4 and se(b1) = 1.0. Consider the hypotheses: [You may find it useful to reference the t table.] Ho: β1 = 0 HA: β1 ≠ 0 a-1. Calculate the value of the test statistic: (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places:) Test statistic a-2. Find the p-value p-value > 0.10 0.05 < p-value < 0.10 0.025 < p-value < 0.05 p-value < 0.025
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