A line of best fit is a straight line that is the best approximation of the given set of data. Show It is used to study the nature of the relation between two variables. (We're only considering the two-dimensional case, here.) A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible). A more accurate way of finding the line of best fit is the least square method . Use the following steps to find the equation of line of best fit for a set of ordered pairs ( x 1 , y 1 ) , ( x 2 , y 2 ) , ... ( x n , y n ) . Step 1: Calculate the mean of the x -values and the mean of the y -values. X ¯ = ∑ i = 1 n x i n Y ¯ = ∑ i = 1 n y i n Step 2: The following formula gives the slope of the line of best fit:
Step 3: Compute the y -intercept of the line by using the formula:
Step 4: Use the slope m and the y -intercept b to form the equation of the line. Example: Use the least square method to determine the equation of line of best fit for the data. Then plot the line.
Solution: Plot the points on a coordinate plane .
 Calculate the means of the x -values and the y -values. X ¯ = 8 + 2 + 11 + 6 + 5 + 4 + 12 + 9 + 6 + 1 10 = 6.4 Y ¯ = 3 + 10 + 3 + 6 + 8 + 12 + 1 + 4 + 9 + 14 10 = 7 Now calculate x i − X ¯ , y i − Y ¯ , ( x i − X ¯ ) ( y i − Y ¯ ) , and ( x i − X ¯ ) 2 for each i .
Calculate the slope. m = ∑ i = 1 n ( x i − X ¯ ) ( y i − Y ¯ ) ∑ i = 1 n ( x i − X ¯ ) 2 = − 131 118.4 ≈ − 1.1 Calculate the y -intercept. Use the formula to compute the y -intercept. b = Y ¯ − m X ¯ = 7 − ( − 1.1 × 6.4 ) = 7 + 7.04 ≈ 14.0 Use the slope and y -intercept to form the equation of the line of best fit. The slope of the line is − 1.1 and the y -intercept is 14.0 . Therefore, the equation is y = − 1.1 x + 14.0 . Draw the line on the scatter plot.
MCQs of Curve fitting by the numerical methodShowing 1 to 10 out of 18 Questions
Showing 1 to 10 out of 18 Questions How do you fit a straight line?Let (x;,yj), t = 0,1,2,....,n be the n sets of observations and let the related relation by y = ax + b. Now we have to select a and b so that the straight line is the best fit to the data. By the principle of least squares, E is minimum.
Which of the following is a normal equation for to fit straight line y a bx *?Fit a straight line y=a+bx into the given data: (x,y):(5,12)(10,13)(15,14)(20,15)(25,16). Thus, the equation of the line is y=11+0.2x.
How do you fit a straight line trend by the method of least squares?Use the least square method to determine the equation of line of best fit for the data. Then plot the line. Straight line equation is y = a + bx. This is the required trend line equation.
What is the formula for curve fitting?The highest-order polynomial that Trendline can use as a fitting function is a regular polynomial of order six, i.e., y = ax6 + bx5 +cx4 + ak3 + ex2 +fx + g. polynomials such as y = ax2 + bx3'2 + cx + + e.
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Fit a straight line for the given pairs of x y which are 0 3 1 6 2 8 3 11 4 13 5 14
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