(a) Use the “p-value” approach to test at the 99% confidence level the statistical significance of all seven regression slope coefficients (i.e., , , , … , ). What is your conclusion? Explain.
Added by Christopher V.
Step 1
.., β7), we need to set up the null and alternative hypotheses: - Null Hypothesis (H0): βi = 0 (the slope coefficient is not statistically significant) - Alternative Hypothesis (H1): βi ≠ 0 (the slope coefficient is statistically significant) Show more…
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3. Derive from first principles using partial differentiation the expressions satisfied by the α, β₁, β₂ and β₃ in the following regression equation: y = α + β₁x₁ + β₂x₂ + β₃x₃ + u Where all symbols have their usual meaning. 4. Suppose you are given the following information: Ŷₜ = 49.6870 - 2.1586Xₜ r² = 0.9757 (0.7463) (0.12113) df=8 T = (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r² tell you? c) Perform a hypothesis using r², such that ρ=0, what do you conclude?
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Consider the following regression results based on 40 observations. [You may find it useful to reference the t table.] Standard p- Coefficients Error t Stat value Intercept 40.4543 12.6945 3.187 0.003 x1 0.9157 0.9382 0.976 0.336 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 b-2. Find the p-value. 0.02 ≤ p-value < 0.05 0.01 ≤ p-value < 0.02 p-value < 0.01 p-value ≥ 0.10 0.05 ≤ p-value < 0.10 c. At the 2% significance level, can we conclude the slope differs from minus one? Yes, since the p-value is less than the significance level. No, since the p-value is more than the significance level. Yes, since the p-value is more than the significance level. No, since the p-value is less than the significance level.
David N.
Simple linear regression based on 32 observations. It is found that hypotheses: and se(b1). 1.2. Consider the Ho: B1 and HA: 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 0.01 0.01 p-value 0.025 At the 5% significance level, what is the conclusion of the test? Do not reject Ho; we may conclude the slope coefficient is less than 10. Do not reject Ho; we may not conclude the slope coefficient is less than 10. Reject Ho; we may not conclude the slope coefficient is less than 10. Reject Ho; we may conclude the slope coefficient is less than 10.
Madhur L.
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