5. The data file TeachingRatings contains data on course evaluations, course characteristics, and professor characteristics for 463 courses at the University of Texas at Austin. A detailed descrip- tion is given in TeachingRatings_Description. One of the characteristics is an index of the professor's "beauty" as rated by a panel of six judges. In this exercise, you will investigate how course evaluations are related to the professor's beauty. (a) Run a regression of average course evaluations (Course_Eval) on the professor's beauty (Beauty). What is the estimated intercept? What is the estimated slope? Explain why the estimated intercept is equal to the sample mean of Course Eval. (Hint: What is the sample mean of Beauty?) (b) Professor Watson has an average value of Beauty, while Professor Stock's value of Beauty is one standard deviation above the average. Predict Professor Stock's and Professor Watson's course evaluations. (c) Does Beauty explain a large fraction of the variance in evaluations across courses? Explain.

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Q: could you explain the steps you took to get there ?

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Q: (1,-16) and (-3,12)

A: To write down the equation of the straight line joining the two given points.

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A: The solution is shown in step-2

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A: The standard deviation is 0.2.

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Q: 5x-20 50

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Q: prow $ PCC-AIB)= pccl B) - p(AIB)

A: The answer is given below

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A: We will use standard matrix of reflection rotation and projection

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A: We have find the integral of  4) ∫x4 exdx5) ∫x5 exdx

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A: The dot product of a=a1, a2, a3 and b=b1, b2, b3 is: a·b=a1b1+ a2b2+ a3b3

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A: x2=y-2-1=z4