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Why does the slope of my line fit plot not match the coefficient of the same variable in my regression?

For one of the variables, the coefficient is positive while the line fit plots trendline is negative.

Using Excel's regression tool... The line best fit plot is for Variable D

EDIT: Regression results Line Best Fit Plot

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  • $\begingroup$ Without a reproducible example there is no way we can tell. You need to be more specific and show at least a snipped of the data so others here can understand what went wrong. $\endgroup$
    – Andy
    Jul 31, 2015 at 22:18
  • $\begingroup$ Just added screen shots, hopefully that provides enough insight. $\endgroup$
    – Derek
    Jul 31, 2015 at 22:33
  • $\begingroup$ What is A-H here? I looks like you are looking at only two dimensions X and Y in the plot above, yet your model seems to include an intercept and coefficients A through H. $\endgroup$
    – StatsStudent
    Jul 31, 2015 at 23:27
  • $\begingroup$ @StatsStudent are you implying that you'd like to see the line fit plots for the other variables? The reason why I am including only variable D's plot is because it has the behavior that I can make the least sense of. From a purely mathematical point of view, I thought that the "coeffecient in a regression" is always equal to the slope of the line fit plot's trendline $\endgroup$
    – Derek
    Aug 3, 2015 at 15:50

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The coefficients from the multiple linear regression are correct. You cannot just add all of the individual trend lines to get the overall trend line. The multiple linear regression attempts to minimize the error term while accounting for all of the variables.

An example of this is if you were to gather data on riding your bike. Let X1 = gear, X2 = pedal speed, and Y = bike travel speed. We know pedal speed is directly related to travel speed. However, when you upshift gears you don't pedal as fast.

If you were to look at X2 vs Y then it would show that pedaling faster decreases travel speed. This is why we must use multiple linear regression on all the variables that affect Y to get their true coefficients.

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