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)
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Professor #
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1
|
2
|
3
|
4
|
5
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6
|
7
|
8
|
9
|
10
|
|
Y
|
3.1
|
3.4
|
3.8
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2.7
|
4.4
|
4.8
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2.5
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1.6
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4.5
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4.9
|
|
X
|
2.8
|
2.4
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3
|
3.4
|
3.8
|
3.8
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2.5
|
1.7
|
4.6
|
4
|
(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.