(7 points) In lecture, we spent a great deal of time talking about simple linear regression,...
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(7 points) In lecture, we spent a great deal of time talking about simple linear regression, which you also saw in Data 8. To briefly summarize, the simple linear regression model assumes that given a single observation x, our predicted response for this observation is ŷ=00+01. (Note: In this problem we write (0,01) instead of (a, b) to more closely mirror the multiple linear regression model notation.) In Lecture 9 we saw that the 0 = 0 and 0₁ = ₁ that minimize the average L₂ loss for the simple linear regression model are: 0 =ÿ - 0₁ Ty 6₁ = = T Or, rearranging terms, our predictions ŷ are: σ x-x ŷ= y + ro₂ 02 (a) (2 points) As we saw in lecture, a residual e, is defined to be the difference between a true response y, and predicted response ₁. Specifically, e;= y. Note that there are n data points, and each data point is denoted by (xi, Yi). Show, using the equation for y above, that the average prediction is also the average value of the response, i.e. | Σ1 y = Η Σ (7 points) In lecture, we spent a great deal of time talking about simple linear regression, which you also saw in Data 8. To briefly summarize, the simple linear regression model assumes that given a single observation x, our predicted response for this observation is ŷ=00+01. (Note: In this problem we write (0,01) instead of (a, b) to more closely mirror the multiple linear regression model notation.) In Lecture 9 we saw that the 0 = 0 and 0₁ = ₁ that minimize the average L₂ loss for the simple linear regression model are: 0 =ÿ - 0₁ Ty 6₁ = = T Or, rearranging terms, our predictions ŷ are: σ x-x ŷ= y + ro₂ 02 (a) (2 points) As we saw in lecture, a residual e, is defined to be the difference between a true response y, and predicted response ₁. Specifically, e;= y. Note that there are n data points, and each data point is denoted by (xi, Yi). Show, using the equation for y above, that the average prediction is also the average value of the response, i.e. | Σ1 y = Η Σ
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Operations management in the supply chain decisions and cases
ISBN: 978-0077835439
7th edition
Authors: Roger G Schroeder, M. Johnny Rungtusanatham, Susan Meyer Goldstein
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