How to analyze the linear regression graph
Good job with running linear regression in Excel.
Now is the time that we analyze the linear regression trendline formed above.
A linear trendline in Excel can take the following three shapes:
Positive trendline (upward facing)
If your trendline is upward facing (it elevates as it goes from left to right), it denotes a positive trend.
This means that there exists a positive relationship between both variables. An increase in the independent variable causes the dependent variable to increase.
This is how your graph will look with a positive trendline to it.
Negative trendline (downward sloping)
If your trendline is downward sloping (it slopes down as it goes from left to right), it denotes a negative trend.
A negative trendline means a negative relationship between both variables.
When there is a negative relationship between two variables, an increase in the independent variable causes the dependent variable to decrease.
This is how your graph will look with a negative trendline to it.
Jog down your memory lane to remember the trendline type in our example above. It was also a downward-sloping (negative) trendline.
That’s because there exists a negative relationship between sales and temperature. As the temperature falls, sales increase.
The two variables can also be independent of each other. In this case, movement in both variables is random with no relation to each other.
As there exists no relationship between them (neither positive nor negative), there is no particular slope for the trendline between them (neither upward facing nor downward sloping).
Such a trendline might look like this.
The trendline above is not exactly horizontal but very close to that. This is because there is no relation between the variables.
The slope of the graph
What if we want to know the percentage of change in Y caused by a change in X?
For example, for every 1% decrease in temperature, sales increase by what percentage?
The slope of the graph is an answer to this. Remember the linear regression equation?
Y = a + bx
In the above equation, the slope is represented by “b”. And the linear regression equation for our example turned out as follows:
Y= 612.77 – 19.622x
Here, the value for b is -19.622 and so is our slope. This means that a 1% change in the X variable (the temperature) causes a -19.622% change in the Y variable (the sales).
Also, as the sign with the value for b is a minus sign, this means that a 1% decrease in Variable X (temperature) causes a 19.622% increase in Variable Y (Sales).