# Average Slope of 4 Slopes

I want to calculate tha Average Slope of 4 Slopes, but Im not too sure if this will require me to calculate the Average error when I do calculate the average of the 4 slopes.

Im obviously calculating the Average as (slope $i := s_i$): $$\frac{s_1+s_2+s_3+s_4}{4}$$

But will the average Slope result if $m=2.6$ as an example, in this have same effect on $Y$ when $X$ is decreased or increased?, obviously based on the equation: $y=mx+b$

My main and ultimate goal is to determine the relationship of $Y$ and $X$ from the equation.

An example of what I am looking for, the Average of the 4 Slopes is 2.989 for example, and I had X was the value of Experience at a workplace and Y was the Salary, what would the Average result of +2.989 for the relationship of work experience and Salary for example?

If this was a normal calculation of y=mx+b then I wouldve said that for each unit increase in the input variable x (Experience), the output y (Salary) increases by 2.989 units, BUT in this case its different, as I have the average of 4 calculated slopes.

• Welcome to MSE! Make sure to keep the variable names the same for precision (in general, people might think $X \neq x$). – gnometorule Mar 3 '13 at 8:19
• Hi @gnometorule, Thanks for the edit, I'll keep that in mind from now on when posting a question. – I AM L Mar 3 '13 at 8:23
• Please let me know if this question doesnt make sense. – I AM L Mar 3 '13 at 8:51
• (1) When you say "error", what exactly do you mean? (2) Is this some form of regression? (3) If you have a linear functional relationship as here, raising and lowering the value of $X$ will have the same impact, but (4) Where did you get these 4 slopes from? – gnometorule Mar 3 '13 at 9:47
• @gnometorule I got the 4 slopes from calculating the Slope(Y,X) in excel for 4 different decades (I have modified my question to make this clearer), So the Average of the 4 Slopes which is +2.989 indicates that there is no positive or negative change to Y?, How so?, All I want to know is what the value means for the relationship for Y and X, Please ignore the "error" that I had mentioned in the question. – I AM L Mar 3 '13 at 11:38

## 1 Answer

It's very hard to figure out what you are doing. Here's my guess. You have $5$ $x$-values, $x_1\lt x_2\lt\cdots\lt x_5$, and corresponding $y$-values, $y_1,\dots,y_5$, and you have calculated the slopes $$s_i={y_{i+1}-y_i\over x_{i+1}-x_i}$$ for $i=1,2,3,4$ and now you want to know what the number $$S={s_1+\cdots+s_4\over4}$$ tells you about the relation between $y$ and $x$.

If this is your question, then I would say $S$ tells you very little of interest about the relation between $y$ and $x$. You are better off learning about "linear least squares fit" which will give you the best fit of the form $y=mx+b$ to your data points.

• Your correct about my question and if S doesnt tell me much about the relationship between Y and X for all the 4 decades calculated of the 4 Slopes, what could be the reason? and yes I am aware I can use the "linear least squares fit" but I need to explain why S wont tell me much about the relationship first, if it was One Slope I could easily calculate the Y Intercept and explain the relationship fully.. – I AM L Mar 3 '13 at 11:50
• Suppose your data points were $(0,0),(10,10),(11,0)$. Then your slopes would be $1$ and $-10$; your "average slope", $-4.5$. Now, does $-4.5$ give you a useful insight into the relation between $y$ and $x$ in this example? – Gerry Myerson Mar 3 '13 at 12:15
• haha, Thanks Gerry, it's what they want me to show with one sentence, I was finding it very difficult to say how an Average of 4 Slopes cannot help us in determining the relationship between X and Y in this matter, Im still a bit confused as to why the question was asked to me until now, if in fact it wont help us at all. – I AM L Mar 3 '13 at 12:22
• Just a a quick clarification, are we dealing with Multiple Linear Regression here? – I AM L Mar 3 '13 at 12:38
• I think multiple linear regression refers to functions of several variables, whereas here we are dealing with a function of a single variable. – Gerry Myerson Mar 3 '13 at 22:32