Show that the following expressions are true:i. ∑ni=1(xi − ¯x) = 0ii. ∑ni=1(xi − ¯x)2 = ∑ni=1 x2i − n ¯x2iii. ∑ni=1(xi − ¯x)(yi − ¯y) = ∑ni=1 xiyi − n ¯x ¯

Question

Show that the following expressions are true:i. ∑ni=1(xi − ¯x) = 0ii. ∑ni=1(xi − ¯x)2 = ∑ni=1 x2i − n ¯x2iii. ∑ni=1(xi − ¯x)(yi − ¯y) = ∑ni=1 xiyi − n ¯x ¯
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Solution 1

Sure, let's go through these one by one:

i. ∑ni=1(xi − ¯x) = 0

This is true because ¯x is the mean (average) of all xi. So, when you subtract the mean from each xi and then sum them all up, the result is zero. This is because the sum of the deviations of the data points from their mean is always z Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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