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The computer-science aptitude score, x, and the achievement score, y (measured by a comprehensive final), were...

The computer-science aptitude score, x, and the achievement score, y (measured by a comprehensive final), were measured for 10 students in a beginning computer-science course. The results were as follows. Calculate the estimated standard error of regression, sb1. (Give your answer correct to two decimal places.)

x 17 20 21 20 7 7 15 19 22 7
y 24 26 23 30 24 15 32 33 19 18
math   Statistics-And-Probability   
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Answer #1

Here 10 observations are given on (x-computer science aptitude score, y-achievement score) We fit a linear modelon the data The model is y.-As + A xi + εί ; i-112 ,10 εϊ is the random error associated with yi , i independent with each other with E(q )-0 and V(q)-σ2,Vi.02 is unknown. We estimate βο and A by the method of ordinary least squares (OLS) which involves minimizing the quantity ΣOz-As-A x.)2 with respect toßo and A. Based on the data the fitted regression equation ofy on x is );-17.52 + 0.44 xil-112, ,10 ; so β.-17.52 and A-0.44 Estimated standard error of the linear regression is calculate by the quantity x5.684 with 8 degrees of freedom

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