# Curve Connecting

I have data point below

{65.7036, 10.3268}, {64.6687, 15.7043}, {63.2802, 20.2614}, {61.5142, 24.8447}, {59.3288, 29.4583}, {56.9188, 33.6827}, {53.8731, 38.1929}, {51.5246, 41.1474}, {47.8597, 43.6472}, {47.6348, 40.8387}, {46.5147, 39.3611}, {45.7298, 37.748}, {44.9824, 36.3016}, {44.3204, 34.9286}, {43.7183, 33.6334}, {43.1688, 32.4031}, {42.6653, 31.2288}, {42.2021, 30.1038}, {41.7727, 29.0247}, {41.3732, 27.9874}, {41.003, 26.9832}, {40.6579, 26.0114}, {40.3355, 25.0688}, {40.0331, 24.1539}, {39.747, 23.2677}, {39.4828, 22.3961}, {39.2326, 21.5487}, {38.9951, 20.7242}, {38.7748, 19.9105}, {38.565, 19.1179}, {38.3677, 18.3395}, {38.1833, 17.5718}, {38.0075, 16.8213}, {37.8425, 16.0814}, {37.6881, 15.35}, {37.5422, 14.6305}, {37.4034, 13.9247}, {37.2743, 13.2241}, {37.1539, 12.5296}, {37.0398, 11.8469}, {36.9337, 11.1692}

I plotted it as shown figure below

My curve expectation is like this

How to make it? How to convert the "new curve" to data points

• So you don't believe your data but you do believe the expected curve? That certainly can be the case. But wouldn't the solution be dealing with the data collection process rather than changing the data to be more consistent to the expected curve? Or am I misinterpreting the objective? – JimB Sep 4 '17 at 5:44

Something like this?

data = {{65.7036, 10.3268}, {64.6687, 15.7043}, {63.2802,
20.2614}, {61.5142, 24.8447}, {59.3288, 29.4583}, {56.9188,
33.6827}, {53.8731, 38.1929}, {51.5246, 41.1474}, {47.8597,
43.6472}, {47.6348, 40.8387}, {46.5147, 39.3611}, {45.7298,
37.748}, {44.9824, 36.3016}, {44.3204, 34.9286}, {43.7183,
33.6334}, {43.1688, 32.4031}, {42.6653, 31.2288}, {42.2021,
30.1038}, {41.7727, 29.0247}, {41.3732, 27.9874}, {41.003,
26.9832}, {40.6579, 26.0114}, {40.3355, 25.0688}, {40.0331,
24.1539}, {39.747, 23.2677}, {39.4828, 22.3961}, {39.2326,
21.5487}, {38.9951, 20.7242}, {38.7748, 19.9105}, {38.565,
19.1179}, {38.3677, 18.3395}, {38.1833, 17.5718}, {38.0075,
16.8213}, {37.8425, 16.0814}, {37.6881, 15.35}, {37.5422,
14.6305}, {37.4034, 13.9247}, {37.2743, 13.2241}, {37.1539,
12.5296}, {37.0398, 11.8469}, {36.9337, 11.1692}};

fit = FindFormula[data, x]
Show[ListPlot[data, PlotStyle -> Green],
Plot[fit, {x, 10, 67}, PlotRange -> All, PlotStyle -> Red]]

• I have additional question, how to convert those curve to data points? – SelfA Sep 4 '17 at 3:51
• @SelfA Table[{x, fit}, {x, 36.9337, 65.7036}] – zhk Sep 4 '17 at 4:05

another option might be to use Fit

Manipulate[
fit=Fit[data,Table[x^m,{m,0,n}],x];

Show[Plot[fit,{x,Min[data[[All,1]]],Max[data[[All,1]]]},PlotStyle->Red],
ListLinePlot[data],PlotRange->All],

{{n,5,"n?"},0,10,1,Appearance->"Labeled"}
]