Chapter 8, Problem 13PE

Program Plan Intro

Regression Line

Program plan:

• Import the header file.
• Define the “graphWin” method
  • Create a window
  • Set the coords
  • Display the message on the window
  • Call the “draw” method for set the point
  • Call the “Line” method for draw the line
  • Call the “draw” method for set the point
  • Call the “Line” method for draw the line
  • Call the “draw” method
  • Call the “Rectangle” method
  • Get the center position
  • Set the “Done” text
  • Call the “draw” method stop the program after clicking the “Done” text
  • Accept the input from the user
  • Set the list
  • Make the condition true
    • Get the mouse action
    • Check the condition
      • Break the loop
    • Otherwise, store user points in an appended list
    • Call the “draw” method
  • Return the result
• Define the “average” method
  • Set the values for the variables
  • Iterate “i” until it reaches “allPoints” value
    • Get the “x” and “y” value
    • Calculate “sumX”, and “sumY”
    • Increment the “count” value
    • Calculate the “sumXiYi, “sqX”, “sumSqXi”, “SqY”, and sumSqYi” values
  • Calculate the “a” and “b” values
  • Return the values
• Define “main” method
  • Display the text on the window
  • Call the “average” method
  • Set the values
  • Call the “Line” method
  • Call the “draw” method
  • Get the mouse action
• Call the function “main()”.

Explanation of Solution

Program:

#import the required header files

from graphics import *

import math as m

#definition of "graphWin" method

def graphWin(Title):

    #Create a graphics window

    win = GraphWin(Title, 400, 400)

    #set the coords

    win.setCoords(-10, -10, 10, 10)

    #tell user to select multiple locations on the screen to designate points

    message = Text(Point(-3, 8), "Click to delineate points on the graph.")

    #draw the point

    message.draw(win)

    #call the "Line" method

    axisX = Line(Point(-10,0), Point(10,0))

    #call the "draw" method

    axisX.draw(win)

    #call the "Line" method

    axisY = Line(Point(0,10), Point(0,-10))

    #call the "draw" method

    axisY.draw(win)

    #call the "Rectangle" method

    r = Rectangle(Point(-9, -9), Point(-7,-8))

    #call the "draw" method

    r.draw(win)

    #get the centre position

    rCenter = r.getCenter()

    #set the text

    stopMouse = Text(rCenter, "Done")

    #call the "draw" method

    stopMouse.draw(win)

    #accept input from user until <done> button is pressed

    click = Point(0,0)

    #set the list

    allPoints = []

    #check the condition

    while True:

        #get the mouse action

        click = win.getMouse()

        #check the condition

        if ((-9 <= click.getX() <= -7) and (-9 <= click.getY() <= -8)):

            #break the loop

            break

        #otherwise

        else:

            #store user points in an appended list

            allPoints.append(click)

            #call the "draw" method

            click.draw(win)

    #return the values

    return allPoints, win

#definition of "average" method

def average(allPoints):

    #set the values for the variables

    sumX = 0

    sumY = 0

    count = 0

    sumXiYi = 0

    sumSqXi = 0

    sumSqYi = 0

    #iterate "i" until it reaches "allPoints" value

    for i in allPoints:

        #get the "x" and "y" value

        x = i.getX()

        y = i.getY()

        #calculate the "sumX" value

        sumX = sumX + x

        #calculate the "sumY" value

        sumY = sumY + y

        #increment the value

        count = count + 1

        #calculate the "xy" value

        xy = x * y

        #calculate the "sumXiYi" value

        sumXiYi = sumXiYi + xy

        #calculate the "SqX" value

        SqX = x * x

        #calculate the "sumSqXi" value

        sumSqXi = sumSqXi + SqX

        #calculate the "SqY" value

        SqY = y * y

        #calculate the "sumSqYi" value

        sumSqYi = sumSqYi + SqY

    #calculate the "a" and "b" value

    a = ((sumY * sumSqXi) - (sumX * sumXiYi)) / (count * (sumSqXi) - sumX ** 2)

    b = ((count * sumXiYi) - (sumX * sumY)) / (count * (sumSqXi) - sumX ** 2)

    #return the values

    return a, b

#definition of "main" method

def main():

    #get the text for the window

    allPoints, win = graphWin("Regression Line")

    #call the method

    a, b = average(allPoints)

    #set the values

    x1 = -10

    x2 = 10

    #call the "Line" method

    regressLine = Line(Point(x1, (a + b * x1)), Point(x2, (a + b * x2)))

    #call the "draw" method

    regressLine.draw(win)

    #get the mouse action

    win.getMouse()

#call the "main" method

main()

Sample Output

Output:

Screenshot of “Regression Line” window

After clicking “Done” button, the below window will appear

Screenshot of “Regression Line” window