[緊急]統計學問題, 求解答 (20分)－航空百科

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[緊急]統計學問題, 求解答 (20分)

發問:

Question about the simple regression and correlationGivenFor # ' s 1 & 2 : n = 20, Σ y = 150.265, Σ xy = 145.212, Σ y^2 = 1170.391, ? = 9.50 - 1.89x, R^2 = 57.3%1. What is the correlation r ?2. Estimate σ^2 = ?3. r = - 0.75 is a weaker correlation than r =... 顯示更多 Question about the simple regression and correlation Given For # ' s 1 & 2 : n = 20, Σ y = 150.265, Σ xy = 145.212, Σ y^2 = 1170.391, ? = 9.50 - 1.89x, R^2 = 57.3% 1. What is the correlation r ? 2. Estimate σ^2 = ? 3. r = - 0.75 is a weaker correlation than r = 0.49 True or False? show the explanation

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最佳解答:

1. beta = -1.89, so we know that r < 0. r2 = R2 for simple linear regression r2 = 0.573 r = -0.7569676347 2. σ2 is estimated by an unbiased estimator s2 (sample variance) s2 = [Σy2 - (Σy)2/n] / (n - 1) s2 = (1170.391 - 150.2652/20) / 19 s2 = 2.179604671 3. False. r = -0.75 means |r| = 0.75 which is a stronger correlation than r = 0.49. When we talk about the strength of a correlation, we consider its absolute magnitude, so whenever it is close to 1 or -1, it is strong, when it is close to 0, it is weak.

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