Find the two closest points for interpolation target_sf = 479.9983 df['distance'] = abs(df['sf'] - target_sf) closest_points = df.nsmallest(2, 'distance')

Extract points for interpolation x1, y1 = closest_points.iloc[0][['sf', 'time']] x2, y2 = closest_points.iloc[1][['sf', 'time']]

Calculate interpolation m = (y2 - y1)/(x2 - x1) y = y1 + m * (target_sf - x1)

print("The interpolated time value for sf = " + str(target_sf) + " is " + str(y) + " seconds") print("
Using points:") print("Point 1: sf = " + str(x1) + ", time = " + str(y1)) print("Point 2: sf = " + str(x2) + ", time = " + str(y2)) print("
Slope = " + str(m)) Let me break down the interpolation process step by step:

For any given sf value (let's call it $x$), we first find the two closest points in our dataset: Find point 1: $(x_1, y_1)$ Find point 2: $(x_2, y_2)$

Calculate the slope between these two points:$m = \frac{y_2 - y_1}{x_2 - x_1}$

Use the point-slope formula to find the interpolated time:$y = y_1 + m(x - x_1)$

Let's use your last example with $\text{sf} = 479.9983$:

Found closest points: Point 1: $(481.4789, 442.1)$ Point 2: $(506.4106, 465.0)$

Calculated slope:$m = \frac{465.0 - 442.1}{506.4106 - 481.4789} = 0.9185$

Applied the formula:y = 442.1 + 0.9185(479.9983 - 481.4789) $$$$ y = 440.74

This method works because it assumes a linear relationship between any two adjacent points. The closer the points are to our target value, the more accurate the interpolation will be.

Would you like to try another example to see how these steps work with different values? Nigiri ☼ — Today at 11:04 The value of ( \text{sf} ) in the context of linear interpolation is a specific point on the x-axis (independent variable) for which we want to estimate or determine the corresponding y-axis (dependent variable) value, such as time. In mathematical terms, if we have a linear relationship between two variables, ( \text{sf} ) represents the input value for which we use the linear equation to find the output value. If you have a specific context or dataset, ( \text{sf} ) would be the variable of interest that you are analyzing or predicting.

The value of ( \text{sf} ) in the context of linear interpolation is a specific point on the x-axis (independent variable) for which we want to estimate or determine the corresponding y-axis (dependent variable) value, such as time. In mathematical terms, if we have a linear relationship between two variables, ( \text{sf} ) represents the input value for which we use the linear equation to find the output value. If you have a specific context or dataset, ( \text{sf} ) would be the variable of interest that you are analyzing or predicting.

149,3259sf = 137,02s 153,1381sf = 140,52s 162,2438 = 148,88s 167,8834 = 154,06s 171,1713sf = 157,08s 177,7257sf = 163,1s 185,7167sf = 170,44s 192,9675sf = 177,1s 200,8064sf = 184,3s 210,6266sf = 193,32s 233,9035sf = 214,7s 260,4683sf = 239,1s 289,7549sf = 266s 305,0406sf = 280,04s 338,3337sf = 310,62s 375,9818sf = 345,2s 410,712sf = 377,1s 440,2163sf = 404,2s 481,4789sf = 442,1s 506,4106sf = 465s 532,7795sf = 489,22s 567,9017sf = 521,48s 591,0044sf = 542,7s 609,0118sf = 559,24s 621,5757sf = 570,78s 642,6751sf = 590,16s 661,5979sf = 607,52 675,6456 = 620,4s 697,4587sf = 640,4 699,291sf = 642,08 701,4723sf = 644,08

Convert 171,3891sf into seconds