Finding the linear regression of data and plotting it

Question

This is for a physics report that I have to hand in. I have a list of two-dimensional data points that approximately form a linear line.

I want to:

1. calculate the best linear fit.
2. put both data points and the linear fit line on a plot
3. put names and units on x and y axis
4. (if possible) put slope and intersection of best fit on plot

Is it possible to do this in Mathematica and if so how?

Example data:

Time, Displacement

    t (s)   d (m)
    0       0
    1       1.9
    2       3.8
    3       5.9
    4       8.1
    5       10.1

Answer 1

Alternatively you might consider using LinearModelFit which allows for extraction of properties such as residuals, influence measures, etc.

data = {{0, 0}, {1, 1.9}, {2, 3.8}, {3, 5.9}, {4, 8.1}, {5, 10.1}};

lm = LinearModelFit[data, x, x];

Another small change from Mr. Wizard's solution is to add the graphics options to Show rather than the individual plots. I find this cleaner in some cases.

Show[ListPlot[data], Plot[lm[x], {x, 0, 5}], 
   AxesLabel -> {"x-name", "y-name"}, PlotLabel -> lm["BestFit"]
]

Answer 2

Basically:

data = {{0, 0}, {1, 1.9}, {2, 3.8}, {3, 5.9}, {4, 8.1}, {5, 10.1}};

Block[{x}, 
 f[x_] = Fit[data, {1, x}, x]
]

-0.119048 + 2.03429 x

Show[
 ListPlot[data, AxesLabel -> {"X data", "Y data"}], (* arbitrary labels *)
 Plot[f[x], {x, Min@#, Max@#}] &@data[[All, 1]]
]

Answer 3

I hope that this will help. The Excel table has the columns titles. I use the following code:

Clear["`*"];
data = Import[SystemDialogInput["FileOpen"], "XLSX"][[1]];
dataDRO = Drop[data, {1}];
xlab = data[[1, 1]];
ylab = data[[1, 2]];
xcol = dataDRO[[All, 1]];
ycol = dataDRO[[All, 2]];

(* Linear model weighted *)
weight = 1/xcol^2;
model = LinearModelFit[dataDRO, x, x, Weights -> weight];
equation = Normal[model];
slope = Select[equation[[2]], # Epsilon Reals &, 1];
intercept = equation[[1]];
predicted = (ycol - intercept)/slope;

(* The table *)
accuracy = predicted*100/xcol;
qwerty = Transpose[Flatten /@ {xcol, ycol, predicted, accuracy}];
Grid[Prepend[qwerty, {xlab, ylab, "Predicted", "% Accuracy"}], 
 Alignment -> Right, Background -> None, 
 Dividers -> {All, {1 -> True, 2 -> True, -1 -> True}}]
Print["y = ", model["BestFit"]]
Print["R2 = ", model["RSquared"]]

(* The plot *)
Show[
 ListPlot[dataDRO, PlotStyle -> PointSize[0.01]],
 Plot[model["BestFit"], {x, 0, Max[xcol]}],
 Frame -> {{True, False}, {True, False}},
 FrameLabel -> {xlab, ylab},
 AspectRatio -> 1/GoldenRatio,
 ImageSize -> 500]