The Statistics of Simple Regression: 4.10-4.11

In this example, we use Mathematica's ability to create Regression or ANOVA tables. This is done by replacing the Fit[] command with the Regress[] command.  Regress is found in the Statistics`LinearRegression package.

Needs["Statistics`LinearRegression`"]

Clear[elk, data, x];

\(elk = {1627, 1527, 1140, 1322, 1431, 1733, 1131, 1611, 1644, 1991, 
        1762, 1076, 1442, 1800, 1667, 1558, 1396, 1753, 1453, 1804}; 

    year = {1963, 1964, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 
        1976, 1977, 1978, 1979, 1980, 1981, 1982, 1984, 1985}; 

    data = Table[{year[\([n]\)], elk[\([n]\)]}, {n, 1, 20}]\)

\(p0 = 
      ListPlot[data, PlotStyle -> {PointSize[.02]}, 
        DisplayFunction -> Identity]; 

    p1 = ListPlot[data, PlotJoined -> True, 
        AxesLabel -> {"Quarter", "Bushels"}]; \)

g[x_] = Fit[data, {1, x}, x]

\(p3 = Plot[g[x], {x, 1960, 1990}, DisplayFunction -> Identity]; 

    Show[p0, p3, DisplayFunction -> $DisplayFunction]; \)

Regress[data, {1, x}, x]

russ
       = {{4.620, 4.750}, {4.950, 4.750}, {4.710, 4.140}, {4.380, 4.070}, {
          4.660, 4.380}, {4.780, 4.490}, {4.490, 4.360}, {4.550, 4.330}, {
          4.760, 4.700}, {4.580, 4.080}, {4.720, 4.540}, {4.660, 4.220}, {
          4.760, 4.760}, {4.790, 4.450}, {4.810, 4.680}, {4.880, 4.660}, {
          4.570, 4.460}, {4.460, 4.490}, {4.780, 4.520}, {4.680, 4.430}, {
          4.690, 4.460}, {4.780, 4.470}, {4.560, 4.500}, {4.880, 4.660}, {
          4.500, 4.500}, {5.000, 4.610}, {4.460, 4.390}, {4.690, 4.690}, {
          4.780, 4.420}, {4.490, 4.360}, {4.880, 4.700}, {4.360, 4.450}, {
          4.600, 4.400}, {4.680, 4.730}, {4.570, 4.570}, {4.530, 4.090}, {
          4.530, 4.530}, {4.560, 4.260}, {4.570, 4.050}, {4.520, 3.880}, {
          4.570, 4.100}, {4.550, 3.990}, {4.610, 3.950}, {4.730, 4.780}, {
          4.800, 4.280}, {4.800, 4.570}, {4.470, 4.290}, {4.720, 4.450}, {
          4.570, 4.420}, {4.570, 4.140}, {5.000, 4.690}, {4.560, 4.200}, {
          4.520, 4.310}, {4.500, 4.360}, {4.820, 4.470}, {3.520, 3.820}, {
          4.160, 3.960}, {4.380, 4.330}, {4.380, 4.330}, {4.420, 4.260}, {
          4.420, 4.300}, {4.500, 4.500}, {4.950, 4.850}, {4.880, 4.730}, {
          4.090, 3.990}, {4.560, 4.260}, {4.710, 4.170}, {4.720, 4.680}, {
          4.780, 4.430}, {4.810, 4.450}, {4.530, 3.920}, {4.230, 4.230}, {
          4.530, 4.760}, {4.570, 4.460}, {4.570, 4.520}, {4.650, 4.900}, {
          4.650, 4.420}, {4.520, 4.360}, {3.920, 4.070}, {4.600, 4.700}, {
          3.460, 2.940}, {4.230, 4.230}, {4.580, 4.580}, {4.470, 4.180}, {
          3.750, 4.370}, {3.590, 3.590}, {4.350, 4.520}, {4.500, 4.370}, {
          4.120, 4.500}, {4.830, 4.830}, {4.060, 4.530}, {4.100, 4.370}, {
          3.530, 4.330}, {4.470, 4.710}, {4.440, 4.440}, {4.400, 4.800}, {
          4.070, 4.420}, {4.530, 4.300}, {4.250, 4.440}, {3.680, 3.950}, {
          4.490, 4.330}, {4.500, 4.370}, {4.100, 4.100}, {4.310, 4.180}, {
          4.410, 4.580}, {3.990, 4.040}, {4.000, 4.560}, {4.520, 4.290}, {
          4.610, 4.760}, {4.660, 4.660}, {4.620, 4.500}, {4.930, 4.560}, {
          4.330, 4.110}, {4.450, 4.600}, {4.380, 4.300}, {4.440, 4.330}, {
          4.840, 4.530}, {4.110, 4.220}, {4.740, 4.490}, {4.400, 4.700}, {
          4.450, 3.990}, {4.860, 4.590}, {4.330, 4.490}, {4.830, 4.410}, {
          4.660, 4.160}, {4.630, 4.520}, {4.700, 3.700}, {4.720, 4.130}, {
          3.990, 4.570}, {4.330, 4.180}, {4.350, 4.410}, {4.400, 4.060}, {
          3.950, 4.260}, {4.350, 4.420}, {3.690, 4.150}, {4.380, 3.990}, {
          4.700, 4.400}, {4.910, 4.750}, {4.710, 4.710}, {4.760, 4.530}, {
          4.520, 4.390}, {4.610, 4.610}, {4.600, 4.500}, {3.860, 3.900}, {
          4.400, 4.660}, {4.430, 4.370}, {4.640, 4.420}, {3.920, 4.420}, {
          4.550, 4.770}, {4.370, 4.330}, {4.770, 4.440}, {4.220, 4.140}, {
          4.580, 4.560}, {4.470, 4.470}, {4.620, 4.660}, {4.440, 4.380}, {
          3.850, 4.070}, {2.200, 3.200}, {3.760, 3.850}, {4.090, 4.450}, {
          4.090, 4.330}, {4.640, 4.700}, {4.610, 4.610}, {4.610, 3.990}, {
          4.590, 4.310}, {4.630, 4.310}, {4.720, 4.450}, {4.390, 4.260}, {
          4.540, 4.200}, {4.860, 4.460}, {4.860, 4.560}, {4.680, 4.370}, {
          4.850, 4.280}, {4.800, 4.800}, {5.000, 4.330}, {3.750, 4.370}, {
          3.740, 4.120}, {3.610, 4.380}, {3.550, 3.440}, {4.410, 4.410}, {
          4.070, 4.420}, {4.400, 4.200}, {4.660, 4.580}, {3.250, 3.750}, {
          3.550, 4.620}, {3.950, 4.710}, {3.430, 4.120}, {3.660, 4.770}, {
          3.660, 4.770}, {3.880, 4.300}, {3.500, 4.490}, {2.780, 3.310}, {
          4.100, 4.420}, {4.480, 4.400}, {4.330, 4.410}, {5.000, 4.810}, {
          4.940, 4.680}, {4.950, 4.860}, {4.960, 4.690}, {4.960, 4.800}, {
          4.930, 4.530}, {5.000, 4.450}, {4.880, 4.660}, {5.000, 4.880}, {
          5.000, 4.790}, {4.920, 4.920}, {4.920, 4.850}, {4.880, 4.660}, {
          4.850, 4.750}, {4.840, 4.890}, {4.260, 3.680}, {4.780, 4.630}, {
          4.580, 4.440}, {4.700, 4.540}, {4.760, 4.700}, {4.760, 4.680}, {
          4.660, 4.800}, {4.400, 4.360}, {4.600, 4.150}, {4.530, 4.460}, {
          3.680, 3.870}, {4.070, 4.140}, {3.900, 4.520}, {3.990, 4.280}, {
          4.450, 4.750}, {4.000, 4.200}, {4.090, 4.090}, {3.630, 3.890}, {
          4.420, 4.680}, {3.930, 4.310}, {4.270, 4.220}, {4.150, 4.050}, {
          4.240, 4.200}, {3.880, 4.230}, {4.260, 4.190}, {4.310, 4.260}, {
          4.400, 4.440}, {4.460, 4.260}, {4.620, 5.000}, {4.090, 4.220}, {
          4.500, 4.600}, {4.360, 4.270}, {4.540, 4.540}, {3.690, 4.230}, {
          4.500, 4.600}, {4.500, 4.500}, {4.660, 4.660}, {3.890, 3.840}, {
          4.490, 4.490}, {4.810, 4.560}, {4.550, 4.550}, {4.280, 4.450}, {
          4.850, 4.420}, {4.420, 4.640}, {3.990, 4.120}, {4.120, 4.520}, {
          4.200, 4.440}, {4.250, 4.100}, {4.510, 4.750}, {4.450, 4.270}, {
          4.630, 4.450}, {4.660, 4.700}, {4.650, 4.390}, {4.650, 4.760}, {
          4.570, 4.730}, {4.060, 4.510}, {4.750, 4.650}, {4.810, 4.680}, {
          4.490, 4.490}, {3.730, 3.840}, {4.430, 4.620}, {4.470, 4.360}, {
          4.420, 4.050}, {4.330, 4.610}, {4.290, 4.450}, {4.240, 4.160}, {
          4.180, 4.140}, {4.050, 4.300}, {4.240, 4.280}, {4.600, 4.300}, {
          4.340, 4.130}, {4.410, 4.290}, {4.590, 4.360}, {4.050, 4.470}, {
          4.230, 4.180}, {3.740, 4.200}, {3.410, 3.680}, {3.830, 4.050}, {
          3.840, 3.920}, {4.000, 4.120}, {4.160, 4.250}, {4.260, 4.420}, {
          4.450, 4.700}, {4.460, 4.380}, {3.810, 3.880}, {4.500, 4.560}, {
          3.660, 3.880}, {4.750, 4.580}, {3.580, 4.040}, {4.700, 4.400}, {
          4.490, 4.130}, {4.150, 4.530}, {4.450, 4.090}, {4.040, 4.400}, {
          4.500, 3.870}, {4.300, 4.200}, {4.440, 4.420}, {4.280, 4.200}, {
          4.260, 4.080}, {4.090, 4.180}, {4.380, 3.920}, {3.990, 4.410}, {
          4.310, 4.630}, {4.180, 4.450}, {4.740, 4.910}, {4.200, 4.550}, {
          3.690, 4.380}, {4.180, 4.620}, {4.070, 4.230}, {4.060, 4.210}, {
          3.760, 4.650}, {3.330, 3.460}, {4.600, 4.400}, {4.200, 4.120}, {
          4.130, 4.590}, {3.730, 4.340}, {3.460, 3.860}, {4.660, 4.550}, {
          4.120, 4.390}, {3.990, 4.050}, {3.990, 4.380}, {3.990, 3.860}, {
          4.440, 3.940}, {4.500, 4.120}, {3.570, 3.850}, {4.490, 4.350}, {
          3.730, 3.990}, {4.610, 4.880}, {4.590, 4.590}, {3.610, 3.760}, {
          4.400, 4.200}, {4.400, 4.300}, {4.530, 4.610}, {4.260, 4.160}, {
          4.370, 4.300}, {4.330, 4.000}, {3.990, 4.430}, {4.260, 3.940}, {
          4.350, 4.350}, {4.260, 4.440}, {2.990, 3.520}, {4.440, 4.610}, {
          3.660, 4.280}, {4.250, 4.420}, {3.170, 4.100}, {3.940, 4.310}, {
          4.050, 4.110}, {4.410, 4.720}, {4.160, 4.700}, {3.780, 4.140}, {
          4.410, 4.700}, {4.220, 4.110}, {4.060, 4.660}, {4.200, 4.240}, {
          4.110, 4.270}, {4.040, 4.150}, {3.930, 3.930}, {2.280, 3.760}, {
          4.300, 4.700}, {4.310, 4.560}, {3.990, 4.220}, {3.200, 3.850}, {
          4.560, 4.430}, {3.930, 4.180}, {3.860, 3.990}, {3.780, 4.210}, {
          3.380, 3.770}, {3.520, 4.100}, {4.080, 4.330}, {4.570, 4.730}, {
          3.990, 4.590}, {4.760, 4.530}, {3.410, 4.240}, {3.600, 4.200}, {
          4.070, 4.530}, {4.000, 4.150}, {3.940, 4.270}, {3.900, 4.350}, {
          3.880, 4.330}, {3.770, 4.110}, {3.430, 4.000}, {4.180, 4.030}, {
          3.650, 4.050}, {3.870, 4.200}, {4.600, 4.600}, {4.540, 3.810}, {
          4.420, 4.240}, {4.580, 4.290}, {4.060, 4.330}, {4.600, 4.160}, {
          4.420, 4.280}, {4.530, 4.530}, {4.490, 4.050}, {4.460, 4.390}, {
          4.060, 4.330}, {4.260, 3.940}, {4.640, 4.410}, {4.460, 4.310}, {
          4.450, 4.360}, {4.660, 4.770}, {5.000, 4.800}, {4.620, 4.620}, {
          4.660, 4.490}, {4.450, 4.210}, {4.680, 4.370}, {4.680, 4.430}, {
          4.680, 4.500}, {4.520, 4.630}, {4.690, 4.300}, {4.610, 4.440}, {
          4.520, 3.920}, {4.490, 3.860}, {4.570, 4.730}, {3.580, 4.160}, {
          4.630, 4.270}, {4.440, 4.290}, {4.660, 4.410}, {4.570, 4.310}, {
          4.480, 4.250}, {4.510, 4.240}, {4.500, 4.830}, {4.480, 4.290}, {
          4.590, 4.330}, {4.400, 4.320}, {4.380, 4.140}, {4.870, 4.750}, {
          4.360, 4.090}, {4.370, 4.370}, {4.500, 4.500}, {4.520, 3.990}, {
          4.380, 4.660}, {4.540, 4.270}, {4.210, 4.140}, {4.160, 4.050}, {
          4.330, 3.990}, {4.090, 3.950}, {4.630, 4.450}, {4.810, 4.870}, {
          4.530, 4.460}, {4.410, 4.080}, {4.590, 3.990}, {4.590, 4.390}, {
          3.860, 3.930}, {4.250, 4.560}, {4.290, 4.470}, {4.700, 4.800}, {
          4.620, 4.370}, {4.400, 4.250}, {4.300, 4.230}, {4.600, 4.800}, {
          4.370, 4.180}, {4.600, 4.700}, {4.850, 4.850}, {4.380, 4.360}, {
          4.120, 4.870}, {4.550, 4.270}, {4.260, 3.990}, {4.160, 4.220}, {
          4.490, 4.240}, {4.880, 5.000}, {4.370, 4.370}, {4.260, 3.940}, {
          4.410, 4.170}, {4.050, 4.000}, {4.550, 3.660}, {4.500, 4.500}, {
          4.530, 4.390}, {4.230, 4.300}, {4.330, 4.350}, {4.140, 4.350}, {
          4.760, 4.690}, {4.230, 3.870}, {4.230, 3.760}, {4.380, 4.220}, {
          4.240, 4.410}, {4.490, 4.570}, {3.990, 4.270}, {3.770, 4.220}, {
          3.810, 3.750}, {3.480, 3.030}, {3.840, 3.920}, {3.800, 3.760}, {
          4.000, 3.900}, {4.330, 3.710}, {3.660, 3.330}, {3.380, 4.070}, {
          3.910, 4.080}, {4.080, 3.740}, {3.200, 3.900}, {3.460, 3.690}, {
          4.240, 3.910}, {4.100, 4.300}, {3.620, 3.500}, {4.140, 3.420}, {
          4.500, 3.500}, {3.610, 3.800}, {3.700, 3.990}, {4.490, 4.040}, {
          2.610, 2.520}, {3.760, 3.990}, {3.360, 3.540}, {3.440, 3.990}, {
          3.900, 4.150}, {4.150, 3.760}, {3.850, 2.570}, {3.760, 3.610}, {
          3.870, 3.240}, {3.500, 4.100}, {3.880, 3.660}, {4.230, 3.920}, {
          3.810, 3.990}, {3.950, 4.040}, {4.140, 3.950}, {3.720, 3.900}, {
          3.700, 3.400}, {4.310, 3.660}, {3.490, 3.270}, {3.370, 3.410}, {
          3.260, 3.530}, {4.350, 4.450}, {4.050, 3.950}, {3.830, 3.770}, {
          3.250, 3.450}, {3.600, 3.100}, {3.570, 3.180}, {3.000, 3.050}, {
          3.530, 3.030}, {3.500, 3.400}, {3.940, 4.200}, {4.270, 3.720}, {
          3.460, 2.760}, {3.180, 3.990}, {3.090, 3.040}, {3.860, 4.220}, {
          2.730, 1.820}, {3.910, 3.740}, {4.120, 3.910}, {4.150, 3.800}, {
          4.030, 3.990}, {3.440, 3.490}, {4.250, 3.870}, {4.170, 4.470}, {
          4.120, 4.690}, {3.750, 4.430}, {4.470, 4.820}, {3.640, 4.580}, {
          3.690, 3.910}, {4.650, 4.340}, {4.520, 4.700}, {4.350, 4.440}, {
          3.800, 4.330}, {4.580, 4.640}, {4.640, 4.640}, {4.680, 4.540}, {
          4.420, 4.520}, {4.250, 4.870}, {4.200, 4.200}, {4.270, 4.450}, {
          4.240, 4.660}, {4.200, 4.700}, {3.940, 4.440}, {4.470, 4.570}, {
          4.710, 4.850}, {4.560, 4.720}, {4.500, 4.500}, {4.550, 4.650}, {
          4.520, 4.840}, {4.530, 4.780}, {3.880, 3.820}, {4.720, 4.850}, {
          4.420, 4.850}, {4.400, 4.800}, {4.460, 4.520}, {4.420, 4.710}, {
          4.490, 4.700}, {3.750, 4.500}, {3.420, 4.380}, {4.400, 4.630}, {
          4.940, 4.890}, {4.580, 4.330}, {4.770, 4.770}, {4.120, 4.470}, {
          4.800, 4.850}, {4.720, 4.640}, {4.720, 4.440}, {4.710, 4.850}, {
          4.500, 4.750}, {4.810, 4.900}, {4.560, 4.620}, {4.440, 4.800}, {
          4.880, 4.770}, {4.760, 4.910}, {4.060, 4.230}, {4.350, 5.000}, {
          4.660, 4.910}, {4.640, 4.760}, {4.600, 4.740}, {4.880, 4.770}, {
          4.460, 4.530}, {4.500, 4.620}, {4.450, 4.630}, {4.080, 4.240}, {
          4.440, 4.520}, {4.540, 4.490}, {4.730, 4.690}, {4.680, 4.620}, {
          4.300, 4.550}, {4.140, 4.780}, {5.000, 5.000}, {4.570, 4.420}, {
          4.800, 4.800}, {4.310, 4.620}, {4.450, 4.540}, {4.300, 4.500}, {
          3.420, 4.710}, {3.990, 4.420}, {4.380, 3.990}, {4.330, 4.460}, {
          4.180, 4.720}, {4.000, 4.120}, {4.520, 4.520}, {3.920, 4.760}, {
          3.850, 5.000}, {4.370, 4.750}, {3.850, 4.400}, {3.780, 4.310}, {
          3.850, 4.710}, {4.370, 4.870}, {4.660, 4.880}, {3.710, 3.780}, {
          4.500, 5.000}, {3.690, 4.610}, {3.890, 4.470}, {3.930, 4.500}, {
          4.500, 5.000}, {4.500, 4.660}, {4.280, 4.570}, {4.550, 4.660}, {
          4.710, 4.710}, {4.550, 4.830}, {4.500, 4.700}, {4.500, 4.800}, {
          3.990, 3.990}, {3.500, 3.800}, {4.350, 4.460}, {3.830, 4.550}, {
          3.800, 4.000}, {4.420, 4.570}, {4.240, 4.450}, {4.530, 4.530}, {
          4.940, 4.880}, {4.610, 4.760}, {3.990, 4.490}, {4.240, 4.580}, {
          4.230, 4.230}, {4.610, 4.800}, {4.630, 4.680}, {4.360, 4.780}, {
          4.260, 4.530}, {3.660, 4.080}, {4.870, 4.500}, {4.340, 4.780}, {
          4.620, 4.500}, {4.320, 4.630}, {4.360, 4.780}, {4.610, 4.490}, {
          4.160, 4.290}, {5.000, 4.500}, {4.710, 4.570}, {5.000, 4.440}, {
          4.660, 4.490}, {4.120, 3.750}, {4.600, 4.450}, {4.440, 3.990}, {
          4.000, 4.450}, {3.740, 3.820}, {4.550, 4.440}, {4.040, 4.410}, {
          3.730, 4.100}, {4.200, 4.150}, {4.040, 4.280}, {4.450, 4.310}, {
          4.260, 4.690}, {4.220, 4.220}, {4.270, 4.610}, {4.190, 4.490}, {
          4.830, 4.490}, {4.230, 3.990}, {4.770, 4.330}, {4.490, 4.330}, {
          4.270, 4.490}, {3.700, 4.290}, {4.210, 4.090}, {4.800, 4.610}, {
          4.560, 4.560}, {4.160, 4.250}, {4.260, 4.360}, {3.900, 4.230}, {
          4.080, 4.210}, {2.280, 2.990}, {3.070, 3.420}, {3.680, 4.040}, {
          4.450, 4.360}, {3.680, 4.160}, {4.800, 4.400}, {4.430, 4.180}, {
          4.380, 3.920}, {3.700, 3.910}, {4.470, 4.520}, {4.490, 4.700}, {
          4.410, 4.520}, {4.500, 4.310}, {4.260, 4.260}, {5.000, 4.660}, {
          4.110, 3.840}, {3.500, 4.250}, {3.870, 4.370}, {4.300, 4.300}, {
          4.590, 4.550}, {3.640, 4.350}, {4.430, 4.560}, {4.000, 4.830}, {
          3.960, 4.320}, {4.530, 4.610}, {4.100, 4.420}, {4.500, 4.560}, {
          3.790, 4.440}, {4.520, 4.560}, {4.660, 4.660}, {3.850, 3.850}, {
          3.720, 4.220}, {3.920, 3.920}, {4.560, 4.390}, {4.550, 4.220}, {
          4.200, 4.120}, {4.640, 4.480}, {4.750, 4.650}, {4.900, 4.700}, {
          4.160, 4.110}, {3.250, 3.660}, {4.520, 4.520}, {3.530, 4.260}, {
          4.290, 4.820}, {3.370, 3.990}, {3.990, 4.580}, {4.310, 4.680}, {
          4.230, 4.660}, {4.000, 4.850}, {4.460, 4.530}, {4.520, 4.680}, {
          3.680, 4.310}, {4.380, 4.840}, {4.110, 4.730}, {4.220, 4.870}, {
          4.150, 4.650}, {3.770, 4.590}, {4.340, 4.260}, {4.330, 4.750}, {
          3.790, 4.580}, {4.380, 4.440}, {4.360, 4.730}, {4.050, 4.290}, {
          4.660, 4.660}, {3.900, 4.360}, {4.500, 4.180}, {4.530, 4.420}, {
          4.050, 4.260}, {4.490, 4.280}, {4.380, 4.610}, {4.490, 4.590}, {
          4.600, 4.400}, {3.880, 4.440}, {4.730, 4.520}, {4.520, 4.610}, {
          4.160, 4.660}, {4.200, 4.450}, {4.750, 4.650}, {4.660, 4.160}, {
          4.330, 4.570}, {3.990, 4.640}, {4.750, 4.600}, {4.720, 4.540}, {
          4.730, 4.500}, {4.600, 4.530}, {4.260, 4.260}, {4.160, 4.220}, {
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          4.690, 4.420}, {4.060, 3.660}, {4.640, 4.350}, {4.530, 4.070}, {
          4.710, 4.280}, {4.620, 4.750}, {4.580, 4.350}, {4.420, 3.990}, {
          4.180, 3.900}, {4.370, 4.310}, {4.370, 4.180}, {4.760, 4.380}, {
          4.300, 4.200}, {4.410, 4.350}, {3.750, 3.950}, {3.890, 4.100}, {
          3.950, 3.820}, {4.120, 3.820}, {4.000, 3.910}, {3.770, 4.520}, {
          3.990, 4.360}, {3.990, 4.170}, {3.460, 4.300}, {3.360, 3.880}, {
          3.330, 4.160}, {3.990, 4.440}, {4.220, 4.220}, {3.960, 4.300}, {
          4.490, 4.620}, {4.100, 4.150}, {3.660, 4.660}, {4.130, 4.520}, {
          3.300, 3.650}, {4.160, 3.990}, {4.000, 4.000}, {4.220, 4.440}, {
          4.460, 4.690}, {2.850, 3.940}, {3.840, 4.220}, {3.690, 3.430}, {
          3.570, 3.140}, {3.590, 4.220}, {3.700, 4.350}, {3.540, 4.400}, {
          3.730, 4.260}, {4.100, 4.100}, {3.840, 4.490}, {4.140, 4.420}, {
          4.110, 4.440}, {3.910, 4.520}, {3.800, 4.350}, {3.790, 3.950}, {
          3.940, 4.440}, {3.730, 4.560}, {3.920, 4.260}, {3.590, 4.510}, {
          3.360, 4.920}, {3.180, 4.620}, {3.180, 4.310}, {3.150, 4.050}, {
          2.650, 4.200}, {3.300, 4.170}, {3.900, 4.500}, {3.950, 4.600}, {
          4.340, 4.600}, {3.990, 4.230}, {3.600, 4.650}, {2.860, 4.260}, {
          4.050, 4.330}, {3.760, 4.230}, {3.600, 3.900}, {3.810, 4.430}, {
          4.260, 4.780}, {4.180, 4.680}, {3.620, 4.550}, {4.000, 4.520}, {
          3.820, 4.260}, {3.480, 4.510}, {3.930, 4.260}, {3.700, 4.120}, {
          4.150, 4.380}, {3.880, 4.440}, {4.380, 4.760}, {4.410, 4.520}, {
          4.140, 4.470}, {4.570, 4.490}, {4.130, 4.440}, {4.060, 4.530}, {
          3.530, 4.460}, {3.990, 4.520}, {3.230, 3.150}, {2.690, 2.760}, {
          3.580, 3.910}, {3.600, 3.900}, {4.090, 4.180}, {3.100, 3.100}, {
          3.110, 3.660}, {3.660, 3.660}, {2.350, 2.990}, {3.300, 3.850}, {
          2.740, 3.210}, {3.090, 3.720}, {3.290, 3.410}, {3.560, 4.120}, {
          2.940, 3.490}, {2.880, 3.050}, {3.530, 4.070}, {3.530, 4.060}, {
          3.610, 3.990}, {3.140, 3.420}, {3.490, 3.990}, {3.540, 2.990}, {
          3.880, 3.990}, {4.070, 3.990}, {4.330, 4.660}, {4.150, 4.100}, {
          3.990, 4.180}, {3.830, 4.490}, {4.110, 4.110}, {3.850, 4.280}, {
          4.090, 4.350}, {3.990, 4.230}, {4.060, 4.260}, {4.070, 4.150}, {
          3.620, 3.740}, {3.750, 3.630}, {4.140, 4.180}, {4.120, 4.430}, {
          4.620, 4.560}, {4.950, 4.300}, {4.800, 4.730}, {4.860, 4.390}, {
          3.500, 3.370}, {4.850, 4.210}, {4.600, 4.330}, {4.350, 4.140}, {
          4.900, 3.810}, {4.890, 4.420}, {3.810, 3.870}, {3.630, 3.810}, {
          3.910, 4.160}, {4.470, 4.270}, {4.500, 4.160}, {3.690, 3.580}, {
          4.350, 4.200}, {4.820, 4.730}, {3.600, 3.540}, {3.400, 3.500}, {
          4.750, 4.490}, {4.570, 4.630}, {4.580, 4.470}, {4.530, 4.530}, {
          4.700, 4.500}, {4.400, 4.000}, {3.840, 4.690}, {3.370, 4.000}, {
          3.940, 4.160}, {4.040, 4.310}, {4.900, 4.600}, {4.850, 4.850}, {
          4.660, 4.550}, {3.500, 3.900}, {4.270, 4.180}, {3.870, 4.500}, {
          4.150, 3.840}, {4.070, 4.280}, {3.440, 3.550}, {4.180, 3.310}, {
          4.380, 4.380}, {4.130, 4.190}, {3.990, 4.450}, {3.870, 4.120}, {
          3.530, 3.990}, {4.450, 4.540}, {2.840, 3.420}, {3.760, 4.300}, {
          3.500, 3.620}, {3.850, 4.420}, {3.300, 3.990}, {4.580, 4.490}, {
          3.290, 3.990}, {3.260, 3.520}, {3.220, 3.770}, {3.730, 4.390}, {
          2.890, 3.310}, {3.760, 3.760}, {3.790, 4.330}, {3.880, 4.580}, {
          4.440, 4.610}, {4.410, 4.520}, {4.180, 4.370}, {4.170, 3.990}, {
          4.330, 4.490}, {3.160, 4.050}, {2.710, 3.210}, {3.690, 3.920}, {
          4.090, 4.090}, {3.300, 3.460}, {4.260, 3.990}, {2.950, 3.550}, {
          3.400, 3.990}, {3.990, 4.110}, {4.580, 3.910}, {3.910, 4.080}, {
          3.150, 3.750}, {4.400, 4.300}, {3.330, 3.920}, {4.060, 4.460}, {
          4.040, 4.370}, {3.280, 4.330}, {2.930, 4.120}, {4.130, 4.310}, {
          4.100, 4.250}};

Regress[russ, {1, x}, x]

\(r0 = 
      ListPlot[russ, PlotStyle -> {PointSize[.02]}, 
        DisplayFunction -> Identity]; 
h[x_] = Fit[russ, {1, x}, x]\)\(r1 = Plot[h[x], {x, 0, 5}, DisplayFunction -> Identity]; 

    Show[r0, r1, DisplayFunction -> $DisplayFunction]; \)