代做STAT3600 Linear Statistical Analysis Class Test代写数据结构程序

STAT3600 Linear Statistical Analysis

Class Test

1. Consider a linear regression model when Y is regressed on X for 21 observations. It is given that

(a) Calculate the least squares estimates of the intercept and the slope.

(b) Prove that where and are the LSE of the intercept and slope, respectively.

(c) Calculate the sum of squared errors and the unbiased estimate of the variance of the error.

(d) Calculate the coefficient of determination. Interpret the result.

2. You are given the following matrices computed for a regression analysis yi = β0 + β1xi1 + β2xi2 + ∈i as

The matrices are properly ordered according to the regression equation given above.

(a) Calculate the least squares estimates of the regression coefficients.Describe the effects of the regressors on the response variable quantitatively.

(b) Construct the analysis of variance table and hence, test whether there is a regression among Y and X1 and X2 at the 5% level of significance. State the alternatives, decision rule and conclusion.

(c) Test the hypothesis that

H0 : β1 = β2

at the 5% level of significance. State the decision rule and conclusion. State the null and alternative hypotheses, decision rule and conclusion.

(d) Estimate the mean Y for two cases where = (0, 1) and = (1, 0). Construct the 95% simultaneous confidence intervals for the expected values by the Scheffes method.