Linear Regression: value for slope












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I'm sorry, I'm new to linear regression so I had a very stupid question. The slope of the best-fit line is defined as the value that minimizes the sum of the squared deviations from each point. Is there any way to prove that there is only one value possible? what if two different values for slope give the same value for the sum? at first i thought that it's a quadratic function, and its minimum value occurs when its derivative is equal to zero, which can have only 1 value since the derivative of a quadratic is a linear.. but then i realised its a sum and has as many variables as the x-values available in the data so i really dont think taking the derivative works.. also unrelated but is there any good source i can learn regression from? most sources skip the basics completely or they dont give any proofs at all.. thanks!






statistics linear-regression







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  • $begingroup$
    Related: stats.stackexchange.com/questions/272376/…
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    – Adam Francey
    Jan 12 at 6:53
















1












$begingroup$


I'm sorry, I'm new to linear regression so I had a very stupid question. The slope of the best-fit line is defined as the value that minimizes the sum of the squared deviations from each point. Is there any way to prove that there is only one value possible? what if two different values for slope give the same value for the sum? at first i thought that it's a quadratic function, and its minimum value occurs when its derivative is equal to zero, which can have only 1 value since the derivative of a quadratic is a linear.. but then i realised its a sum and has as many variables as the x-values available in the data so i really dont think taking the derivative works.. also unrelated but is there any good source i can learn regression from? most sources skip the basics completely or they dont give any proofs at all.. thanks!






statistics linear-regression







share|cite|improve this question









$endgroup$












  • $begingroup$
    Related: stats.stackexchange.com/questions/272376/…
    $endgroup$
    – Adam Francey
    Jan 12 at 6:53














1












1








1


1



$begingroup$


I'm sorry, I'm new to linear regression so I had a very stupid question. The slope of the best-fit line is defined as the value that minimizes the sum of the squared deviations from each point. Is there any way to prove that there is only one value possible? what if two different values for slope give the same value for the sum? at first i thought that it's a quadratic function, and its minimum value occurs when its derivative is equal to zero, which can have only 1 value since the derivative of a quadratic is a linear.. but then i realised its a sum and has as many variables as the x-values available in the data so i really dont think taking the derivative works.. also unrelated but is there any good source i can learn regression from? most sources skip the basics completely or they dont give any proofs at all.. thanks!






statistics linear-regression







share|cite|improve this question









$endgroup$




I'm sorry, I'm new to linear regression so I had a very stupid question. The slope of the best-fit line is defined as the value that minimizes the sum of the squared deviations from each point. Is there any way to prove that there is only one value possible? what if two different values for slope give the same value for the sum? at first i thought that it's a quadratic function, and its minimum value occurs when its derivative is equal to zero, which can have only 1 value since the derivative of a quadratic is a linear.. but then i realised its a sum and has as many variables as the x-values available in the data so i really dont think taking the derivative works.. also unrelated but is there any good source i can learn regression from? most sources skip the basics completely or they dont give any proofs at all.. thanks!






statistics linear-regression




statistics linear-regression






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asked Jan 12 at 6:27









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  • $begingroup$
    Related: stats.stackexchange.com/questions/272376/…
    $endgroup$
    – Adam Francey
    Jan 12 at 6:53


















  • $begingroup$
    Related: stats.stackexchange.com/questions/272376/…
    $endgroup$
    – Adam Francey
    Jan 12 at 6:53
















$begingroup$
Related: stats.stackexchange.com/questions/272376/…
$endgroup$
– Adam Francey
Jan 12 at 6:53




$begingroup$
Related: stats.stackexchange.com/questions/272376/…
$endgroup$
– Adam Francey
Jan 12 at 6:53










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