(1,2),(2,3),(3,4),(4,5),(5,6)We want to find the line 𝑦=𝑚𝑥+𝑐y=mx+c that best fits these data points in the least squares sense, where 𝑚m is the slope and 𝑐c is the y-intercept.
Question
(1,2),(2,3),(3,4),(4,5),(5,6)We want to find the line 𝑦=𝑚𝑥+𝑐y=mx+c that best fits these data points in the least squares sense, where 𝑚m is the slope and 𝑐c is the y-intercept.
Solution
To find the line y = mx + c that best fits these data points in the least squares sense, we need to calculate the slope (m) and the y-intercept (c).
Step 1: Calculate the mean of the x-values and the mean of the y-values. Mean of x (x̄) = (1+2+3+4+5) / 5 = 3 Mean of y (ȳ) = (2+3+4+5+6) / 5 = 4
Step 2: Calculate the slope (m). The formula for m is: m = Σ[(xi - x̄)(yi - ȳ)] / Σ[(xi - x̄)^2] Where: xi and yi are the individual x and y values, x̄ is the mean x value, and ȳ is the mean y value.
Step 3: Calculate the y-intercept (c). The formula for c is: c = ȳ - m*x̄
Step 4: Substitute m and c into the equation y = mx + c to get the line of best fit.
Please note that the above steps are a simplification. In practice, you would use a software or programming language like Python or R to calculate the line of best fit for a large number of data points.
Similar Questions
In choosing the best fitting line through a set of points in a linear regression, we choose the one with the __________. a. smallest sum of squared residuals b. largest sum of squared residuals c. smallest sum of squared error d. a and c
Instructions: Determine the equation of line of best fit for the data. Write your equation in y=𝑦= form. Do NOT include spaces in your answer.x𝑥y𝑦2244557710101212131315151515171720202222Equation:
How is the slope of the line of best fit calculated using the least squares method?Select one:a.By dividing the sum of the y values by the sum of the x valuesb.By dividing the sum of the product of the x values and the y values by the sum of the squares of the x valuesc.By dividing the sum of the product of the x values and the y values by the sum of the x valuesd.By dividing the sum of the y values by the sum of the squares of the x values
Activity (continued from previous page)4. Turn off Show least-squares fit line. Click New r, andsketch the scatter plot to the right.What is the value of r?Turn on Fit a line. Use the slope (m) and y-intercept (b)sliders to estimate the line that fits this data set best.Sketch your line and record its equation below.Equation of estimated line:Check your estimate by turning on Show least-squares fit line. Record the equation for theactual least-squares fit line.Least-squares fit line equation: Was your estimate close?
Given the line of best fit for a set of data points with the equation y = 5x – 2.5, what is the residual for the point (4, 13)?A.13B.4.5C.–13D.–4.5
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