hp-support-head-portlet

Actions
Loading...

Welcome to HP Customer Support

hp-contact-secondary-navigation-portlet

Actions
Loading...

hp-share-print-widget-portlet

Actions
Loading...
  • Information
    We are upgrading our website

    If you experience errors during this time, please try again later. 

    Information
    Looking for Site Help?

    Learn about the features of the HP Customer Support site and how to use them to meet your online support needs. Click Here

     

hp-concentra-wrapper-portlet

Actions
Loading...

HP 12c Platinum Financial Calculator - Statistics - Linear Regression

Linear regression
Linear regression is a statistical method for finding a smooth straight line that best fits two or more data pairs in a sample being analyzed. Any straight line like the one shown in Figure 1 owns two specific coefficients that precisely locate it in a planar coordinate system: a y-intercept A and a slope B. These coefficients compose the straight line equation y = A + Bx. It is also important to mention that the correlation | r | is always 1 when only two points are entered.
Figure : Graph of the line y = A + Bx
HP 12c Platinum statistics
In the HP 12c Platinum, summations resulting from statistics data are suitable for linear regression computations. Given the y and x coordinates of any two or more points belonging to a curve, the linear regression coefficients can be easily found.
Practice solving linear regression problems
Example 1
Based on the information presented in the graphic in Figure 2, compute the y-intercept and slope to characterize the straight line.
  note:
The line crosses the x-axis at the origin (0,0).
Figure : Line passing the origin and the point (4,6)
Solution
One of the points that belongs to the curve is (0,0) and the other one is (4,6). Both must be entered to compute the equation of the line. Be sure to clear the statistics/summation memories before starting the problem.
Keystroke
Display
Figure : Displaying the number of entries
The display shows the number of entries.
Now compute the slope (B) by entering: (Since A is already zero)
Keystroke
Display
Figure : Calculating the slope B
Answer
The expression for this straight line has A=0 and B=1.5. The equation is y = 1.5x + 0.
Example 2
Based on the information presented in the graphic in Figure 5, compute the y-intercept and slope to characterize the straight line. Then use x-forecasting to compute the x-related coordinate for y=5.
Figure : Graph to compute the x-related coordinate when y=5
Solution
Be sure to clear the statistics/summation memories before starting the problem.
Press .
The data pairs must be entered before computing the coefficients.
Keystroke
Display
Figure : Entering the coordinates of the points
As the line does not cross the x-axis at the origin, we forecast y when x=0 to find the y-intercept A:
Keystroke
Display
Figure : Finding the y-intercept when x=0
To compute the slope, now press:
Keystroke (In RPN mode)
Keystroke (In algebraic mode)
Display
Figure : Finding the slope of the line
Now it is necessary to forecast x for y=5.
Keystroke
Display
Figure : Calculating the value of x when y=5
Answer
This straight line has A=1.67 and B=0.33 and its expression is: y = 1.67 + 0.33x.
Example 3
Linear programming is a common technique used to solve operational research problems by graphics inspection. Based on the information presented in the graphics in Figure 10, compute the y-intercept and slope for both straight lines S1 and S2.
Figure : Graph indicating the lines S1 and S2
Solution
Be sure to clear the statistics/summation memories before starting the problem.
Press .
By inspection, the y-intercept for both lines is found to be 3.5 for S1 and 5 for S2. Now we need to compute their slope. The data pairs for S1 are (10,0) and (0,3.5):
Keystroke
Display
Figure : Entering the coordinates of the points for S1
The slope for S1 can be found with the following sequence:
Keystroke (In RPN mode)
Keystroke
Display
Figure : Calculating the slope of line S1
Now, to compute S2 slope it is necessary to clear the statistics/summation memories and enter (5,0) and (0,4.5) as the new data pairs.
Keystroke
Display
Figure : Entering the coordinates of the points for S2
The slope for S2 can be found with the same sequence as before:
Keystroke (In RPN mode)
Keystroke (In algebraic mode)
Display
Figure : Calculating the slope of line S2
Answer
For S1, A = 3.5 and B = -0.35. For S2, A = 5 and B = -0.90.

hp-feedback-input-portlet

Actions
Loading...

hp-online-communities-portlet

Actions
Loading...

Ask the community!


Support Forum

Support Forum

Join the conversation! Find Solutions, ask questions, and share advice with other HP product owners. Visit now


hp-feedback-banner-portlet

Actions
Loading...

hp-country-locator-portlet

Actions
Loading...
Country: Flag Thailand

hp-detect-load-my-device-portlet

Actions
Loading...