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Use hand calculations to fit the multiple linear regression model 1 y = β0 + β1x1 + β2x2 to the

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Use hand calculations to fit the multiple linear regression model 1
y = β0 + β1x1 + β2x2
to the data set in DS 13.6.2.
(a) Write down the vector of observed values of the response variable Y and the design matrix X.
(b) Calculate X'X.
(c) Verify that
Use hand calculations to fit the multiple linear regression model

(d) Verify that β^0 = 4, β^1 = -3, and β^2 = 1.
(e) Calculate the vector of predicted values of the response variable Y and the vector of residuals e.
(f) What is the sum of squares for error?
(g) Show that the estimate of the error variance is σ^2 = 54/7.
(h) What is the standard error of β^1? Of β^2? Should either of the input variables be dropped from the model?
(i) What is the fitted value of the response variable when
x1 = 2 and x2 = -2?
What is the standard error of this fitted value?
(j) Construct a 95% prediction interval for a future value of the response variable obtained with x1 =2 and x2 = -2.

Future Value
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value (FV) is important to investors and financial planners as they use it to estimate how much an investment made today will be worth...
Transcribed Image Text:

73/680-1/136 l/136 0 (XX)-1 =1-1/136

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a b e f SSE 54 h s e 1 0 238 s e 2 0 258 Bot…View the full answer


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Probability And Statistics For Engineers And Scientists

ISBN: 9780495107576

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Question Posted: June 22, 2016 07:40:13
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