Question: In a multiple linear regression model Y = Be + B f1 + B 12 te with en N(0,0), the design matrix X, response vector

In a multiple linear regression model Y = Be + B

In a multiple linear regression model Y = Be + B f1 + B 12 te with en N(0,0), the design matrix X, response vector Y and (XTX)-1 are given below. 5 1 0 1 1 0 2 1 0 3 2 6 1 04 5 1 05 9 X= Y= (XTX)-1 0.65 -0.20 -0.15 -0.20 0.40 0.00 -0.15 0.00 0.05 1 1 1 0 1 1 2 4 5 1 1 3 1 1 4 1 1 5 8 7 (a) (2 points) Please calculate the ordinary least squares estimates of 3 = (B, B1, B2). 1 (b) (2 points) Please calculate the fitted values from this model and further provide an unbiased estimate of the error variance o?. (e) (2 points) Please construct 95% confidence intervals for B, and B2. (d) (2 points) Please test the hypotheses Ho: B2 = 1 vs HQ : B2 # 1. (Hint: One needs to clearly state each step of a complete hypothesis testing process.) (e) (2 points) Please give a point estimate and a 95% confidence interval for the quantity y = Bo + B1 +382. O and r2 = 5 and (f) (2 points) Please predict the response value for a new observation with r give a 95% prediction interval. In a multiple linear regression model Y = Be + B f1 + B 12 te with en N(0,0), the design matrix X, response vector Y and (XTX)-1 are given below. 5 1 0 1 1 0 2 1 0 3 2 6 1 04 5 1 05 9 X= Y= (XTX)-1 0.65 -0.20 -0.15 -0.20 0.40 0.00 -0.15 0.00 0.05 1 1 1 0 1 1 2 4 5 1 1 3 1 1 4 1 1 5 8 7 (a) (2 points) Please calculate the ordinary least squares estimates of 3 = (B, B1, B2). 1 (b) (2 points) Please calculate the fitted values from this model and further provide an unbiased estimate of the error variance o?. (e) (2 points) Please construct 95% confidence intervals for B, and B2. (d) (2 points) Please test the hypotheses Ho: B2 = 1 vs HQ : B2 # 1. (Hint: One needs to clearly state each step of a complete hypothesis testing process.) (e) (2 points) Please give a point estimate and a 95% confidence interval for the quantity y = Bo + B1 +382. O and r2 = 5 and (f) (2 points) Please predict the response value for a new observation with r give a 95% prediction interval

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