# 2. In a linear regression model y=Bo+B,x+ &amp; where X is a ...

## Transcribed Text

2. In a linear regression model y=Bo+B,x+ & where X is a nonrandom regressor, E has mean zero and variance 02. Suppose that n independent paired data (y1, X1), , (yn, Xn) satisfy this model. After fitting this model to a set of n = 25 paired data, we obtain R2=0.90,Syr=50. Construct a 95% prediction value of y at x = X, where x is the sample mean of 25 x's. [20 points] 3. Given the following sample (x, y ) data: (8, 9), (8, 10), (7, 9), (6, 8), (3,6), (4, 8), (4, 8), (5, 9), (5, 7), (6, 9). A simple linear regression model is fitted to these data. [total 35 points] a. Estimate y-intercept and slope. b. Estimate the variance of y. c. Test statistical significance for slope. d. Construct 95% confidence interval of slope. e. Construct ANOVA table for testing slope. f. State assumptions for your analyses in (a)-(e) above. g. What assumptions you describe in f are required for (a)-(e) individually? Discuss your answers in detail.

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