Three observations for a response random variable Y are {4,9,14}; the corresponding values observed for the...

 

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Three observations for a response random variable Y are {4,9,14}; the corresponding values observed for the explanatory vari- able X are {3,4,5}. Assume a linear model: Y = 0 + 31X+ Bo+B1X + (a) Compute ordinary least squares estimates of the coefficients 0 and B using linear algebra calculations by hand and with explanatory comments. (4 marks). (b) Calculate by hand the estimates of the residuals . (4 marks). (c) Perform the same matrix algebra calculations of part (a) and (b) using R. (4 marks). (d) Estimate the coefficients using the function 1m in R. (2 marks).| Three observations for a response random variable Y are {4,9,14}; the corresponding values observed for the explanatory vari- able X are {3,4,5}. Assume a linear model: Y = 0 + 31X+ Bo+B1X + (a) Compute ordinary least squares estimates of the coefficients 0 and B using linear algebra calculations by hand and with explanatory comments. (4 marks). (b) Calculate by hand the estimates of the residuals . (4 marks). (c) Perform the same matrix algebra calculations of part (a) and (b) using R. (4 marks). (d) Estimate the coefficients using the function 1m in R. (2 marks).|