SPSS generation of scatter plots’ trend line

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  • #783
    Mandi Lu
    Participant

    hi everyone! let me start off by saying I am very weak with any and everything remotely mathematical. With that being said, this question comes from a place of deep frustration. I had to use SPSS for an assignment in class. The line of best fit in my scatter plot (generated by SPSS) was not the ‘best’ Anyone could see that a better line could be generated passing through much more points. What can I do to fix this in SPSS? My lecturer told me to draw a manual line and explain…but I do not even know where to begin as I do not understand those equations!! Help me plz! Here is the scatter plot scatterplot.png

    #786
    Dave Collingridge
    Participant

    Mandi,

    The best line would be one that satisfies the criterion of least squares. By the criterion of least squares I mean the prediction line that minimizes the sum of the squared differences between true and predicted values. This is what SPSS probably did when it created a line for your plot. However, looking at your plot the relationship between variables x and y is very weak! When I first saw the plot I thought “no relationship” and thus no best fitting line. Anyway, if saying “no meaningful relationship” does not satisfy your teacher you need to follow these steps to manually draw a line.

    1. Find the prediction equation: predicted y = b(x) +a

    Where:

    “b” is the slope and can be found from b = r * (Sy/Sx), where r=correlation between x and y, Sy=standard deviation of y, etc.

    “a” is the y-intercept and can be found from a = (mean of y – (b * mean of x))

    2. Put a and b values into the prediction equation above.

    3. Put a dot on the y-axis of your plot representing the intercept y-value which is value “a”

    4. Select a high value for x and put it into the formula. You will get a predicted y-value for that x-value. Put a dot on your plot representing the y-value you computed for the x-value you selected.

    5. Connect the two dots. That is your best fitting line. 

    #785
    Mandi Lu
    Participant

    HI Dave

    thanks so much for taking the time to respond to me. I really do not sure why my lecturer is being so difficult bc to me there is no meaningful relationship indeed. Bc I am so unfamiliar with equations and statistics entirely doing it manually would take me forever 🙁 Because I am better with words I am trying to think of a way to verbally explain what SPSS generated and discuss. Sighs Thanks a lot though Dave!!

    #784

    Dave is right – the Rsquare (top right corner) is near zero indicating no relation. When there is no correlation the line of “best fit” ends up as a horizontal line passing through the mean of y. What this is saying is that if you want to predict y with the smallest sum of squared error, then you should predict that everyone has the mean value, regardless of what x might be.  SPSS has drawn it correctly, since the aim is not to actually pass through as many points as possible, but rather to get as close to them as possible, in terms of the vertical distance (i.e. in terms of the y variable).

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