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VCE Further MathsVCE Further MathsLeast Square Regression using the calculator
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Temperature (°C) x 5 10 15 20 25 30 35
No. of Students in a class wearing jumpers
y 18 10 6 5 3 2 2
What is your understanding of this data set? Observe the pattern, look at what’s happening to the dependent and independent variables. You should be able to generalise a relationship.
Step 1: Justifying which variable should be the dependent and independent variable. Explain why.
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Step 2: Performing a Least Square Regression using the calculator.
From MENU select STATISTICS
Enter the independent variable in list1and the dependent variable in list2
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Step 3: Finding the Regression Equation
Select Calc Select linear Reg
Note: Make sure the independent variable is correctly selected in the Xlist and the dependent variable is in the Ylist
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Step 3 Con’t: Reading the gradient (a) and y-intercept (b)The r correlation value can also be read off from this screen
The equation is:y = -0.48x + 16.14
Interpret the meaning of the gradient and y-intercept.
The gradient shows a drop of 0.48 number of students wearing jumpers for every 1 degree increase in the temperature. The y-intercept being the initial number of students wearing jumpers is at 16 when x=0
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Step 4: Plotting the scatterplot
Select the plotting icon from the top menu
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Select the graphing icon from the top menu
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Step 5: Finding the predicted y values
Type in your regression equation here(-0.48List1 +16.14). Replace x with List1.
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Make a note that:
List1 are your x values
List2 are you y values
List 3 are your predicted y values using the regression equation
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Step 6: Finding the residual
Go back to your linear reg screen. Select list4 to place where your residual will be
Remember: The residual is the difference between the original y and the predicted y (y-ypred)
A positive value means under predicted. A negative value means over predicted.
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Step 7: plotting the residual plot (residual vs original x values)
Select the plotting icon Take note: The x values are still in list1 but the residuals are in list4
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Select the graphing icon
The points of the residual plot show a curved pattern, indicating that the original data has a non-linear relationship
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Step 8: TransformationThere are several transformations that you can perform. Examine the points on the original scatterplot and look at the data pattern to decide which one to use.
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According to the data pattern, a reciprocal transformation of the x variable is applied (1/x).
In your list screen, make list5 as your transformed x data
Remember, your original x data was stored in list1
Type 1/list1
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Transformed x data
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Step 9: To find your transformed equation
Remember, your new transformed x data are now in list5
Must provide in the order of independent first, then the dependent
We have only transformed the x data therefore, the original y data remains the same in list2
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The new equation can be read off the screen.
y = 94.58(1/x) – 0.44
r is now 0.99 much improved in terms of the strength of the relationship
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Step 10: Plotting the transformed data
Much better fit!