Definitions of the total sum and squares

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Reference no: EM131132532

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

3

3.4

3.8

3.8

2.5

1.7

4.6

4

(a) Calculate the following X- i=110(Xi - X-)(Yi - Y-) i=110(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.

Reference no: EM131132532

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