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Problem - You have the following sample of data on the quality ratings for undisclosed faculty (Y) versus their rating in terms of perceived easiness (X) (5 = Easy 1 = Hard)
Professor #
1
2
3
4
5
6
7
8
9
10
Y
3.1
3.4
3.8
2.7
4.4
4.8
2.5
1.6
4.5
4.9
X
2.8
2.4
1.7
4.6
(a) Calculate the following X- i=1∑10(Xi - X-)(Yi - Y-) i=1∑10(Xi - X-)2.
(b) Assume that these observation were generated by the following model: Y = β0 + β1X + u , where u is the random error term. Compute OLS estimators β0 and β1 using the formulas derived in class.
(c) Calculate the predicted rating, Y^ and the estimator error u^ = Yi - Y^i for i = 6.
(d) Using the definitions of the Total Sum and Squares (TSS) and the Sum of Squared Residuals (SSR) compute R2 of this regression.
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Multiplicative decomposition method
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Solve the forecast model
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