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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

We want to find the line y=mx+c y = mx + c that best fits these data points in the least squares sense, where m m is the slope and c c is the y-intercept.

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Solution

It seems like you've missed to provide the data points. However, I can guide you through the general steps to find the line of best fit using the least squares method.

  1. First, you need to calculate the mean (average) of your x-values and the mean of your y-values.

  2. Then, subtract the mean of x from each x value (call them "a"), and do the same for y (call them "b").

  3. Multiply each "a" value with its corresponding "b" value and sum them all up. This is the numerator of your slope (m).

  4. Square each "a" value and sum them all up. This is the denominator of your slope (m).

  5. Divide the numerator by the denominator to get the slope (m).

  6. To find the y-intercept (c), subtract m times the mean of x from the mean of y.

The resulting equation is the line of best fit for your data points.

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