Suppose that you are modelling cooling costs (y) as a function of the daily high temperature (x) for a building, using a simple linear regression model. You have data consisting of pairs of observations (x, y) over many years. Suppose that from this data you find a Pearson correlation between x and y of 0.5. If tomorrow the temperature is 3 standard deviations above the mean, how many standard deviations above the mean would you expect the cooling costs to be? If it is true that, tomorrow, the temperature is as given in the previous problem, then the expectation that you gave is the exact cooling cost that will occur. O True O False
Suppose that you are modelling cooling costs (y) as a function of the daily high temperature (x) for a building, using a simple linear regression model. You have data consisting of pairs of observations (x, y) over many years. Suppose that from this data you find a Pearson correlation between x and y of 0.5. If tomorrow the temperature is 3 standard deviations above the mean, how many standard deviations above the mean would you expect the cooling costs to be? If it is true that, tomorrow, the temperature is as given in the previous problem, then the expectation that you gave is the exact cooling cost that will occur. O True O False
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text:Suppose that you are modelling cooling costs (y) as a function of the daily high temperature
(x) for a building, using a simple linear regression model. You have data consisting of pairs of
observations (x, y) over many years. Suppose that from this data you find a Pearson
correlation between x and y of 0.5.
If tomorrow the temperature is 3 standard deviations above the mean, how many standard
deviations above the mean would you expect the cooling costs to be?
If it is true that, tomorrow, the temperature is as given in the previous problem, then the
expectation that you gave is the exact cooling cost that will occur.
True
O False
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