# Tut3 - NATIONAL UNIVERSITY OF SINGAPORE Department of...

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1 NATIONAL UNIVERSITY OF SINGAPORE Department of Statistics and Applied Probability 2013/14 Semester 1 ST3131 Regression Analysis Tutorial 3 1. A regression model 𝑦 = 𝛽 0 + 𝛽 1 𝑥 1 + 𝛽 2 𝑥 2 + 𝜖 was fitted to eleven observations. The data were summarized as follows. ∑ 𝑦 𝑖 𝑖 = 33 ∑ 𝑥 1𝑖 𝑖 = 66 ∑ 𝑥 2𝑖 𝑖 = 22 ∑ 𝑦 𝑖 2 𝑖 = 289 ∑ 𝑥 1𝑖 2 𝑖 = 506 ∑ 𝑥 2𝑖 2 𝑖 = 484 ∑ 𝑥 1𝑖 𝑦 𝑖 𝑖 = 85 ∑ 𝑥 2𝑖 𝑦 𝑖 𝑖 = 142 ∑ 𝑥 1𝑖 𝑥 2𝑖 𝑖 = 346 The inverse of the 𝑋′𝑋 matrix for this problem is given as follows 1 28644 125188 24332 11704 24332 4840 2354 11704 2354 1210 (i) Find the least squares estimates of 𝛽 0 , 𝛽 1 and 𝛽 2 in the model. (ii) Using α = 0.05, test if the overall regression is statistically significant. (iii) Calculate the square of the multiple correlation coefficient. What portion of the total variation is explained by the two predictor variables?

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