import java.io.*;
import java.util.*;
public class LinearRegression {
public static void main(String[] args) {
int MAXN = 1000;
int n = 0;
double[] x = new double[MAXN];
double[] y = new double[MAXN];
// first pass: read in data, compute xbar and ybar
double sumx = 0.0, sumy = 0.0, sumx2 = 0.0;
while(!StdIn.isEmpty()) {
x[n] = StdIn.readDouble();
y[n] = StdIn.readDouble();
sumx += x[n];
sumx2 += x[n] * x[n];
sumy += y[n];
n++;
}
double xbar = sumx / n;
double ybar = sumy / n;
// second pass: compute summary statistics
double xxbar = 0.0, yybar = 0.0, xybar = 0.0;
for (int i = 0; i < n; i++) {
xxbar += (x[i] - xbar) * (x[i] - xbar);
yybar += (y[i] - ybar) * (y[i] - ybar);
xybar += (x[i] - xbar) * (y[i] - ybar);
}
double beta1 = xybar / xxbar;
double beta0 = ybar - beta1 * xbar;
// print results
System.out.println("y = " + beta1 + " * x + " + beta0);
// analyze results
int df = n - 2;
double rss = 0.0; // residual sum of squares
double ssr = 0.0; // regression sum of squares
for (int i = 0; i < n; i++) {
double fit = beta1*x[i] + beta0;
rss += (fit - y[i]) * (fit - y[i]);
ssr += (fit - ybar) * (fit - ybar);
}
double R2 = ssr / yybar;
double svar = rss / df;
double svar1 = svar / xxbar;
double svar0 = svar/n + xbar*xbar*svar1;
System.out.println("R^2 = " + R2);
System.out.println("std error of beta_1 = " + Math.sqrt(svar1));
System.out.println("std error of beta_0 = " + Math.sqrt(svar0));
svar0 = svar * sumx2 / (n * xxbar);
System.out.println("std error of beta_0 = " + Math.sqrt(svar0));
System.out.println("SSTO = " + yybar);
System.out.println("SSE = " + rss);
System.out.println("SSR = " + ssr);
}
}
This is a difficult question to answer. The pure answer is no. In reality, it depends on the level of randomness in the data. If you plot the data, it will give you an idea of the randomness. Even with 10 data points, 1 or 2 outliers can significantly change the regression equation. I am not aware of a rule of thumb on the minimum number of data points. Obviously, the more the better. Also, calculate the correlation coefficient. Be sure to follow the rules of regression. See the following website: http:/www.duke.edu/~rnau/testing.htm
Viewing the data is an easy way to see some of their characteristics such as trends, seasonality, outliers, relationship between variables (linear, quadratic, power etc).
a preconceived idea or prejudice.
Do you not think that, when instructed to "use the table to ... " it would have helped to have at least some idea about the table.Do you not think that, when instructed to "use the table to... " it would have helped to have at least some idea about the table.Do you not think that, when instructed to "use the table to... " it would have helped to have at least some idea about the table.Do you not think that, when instructed to "use the table to... " it would have helped to have at least some idea about the table.
i dont have an idea
Thomas Kuhn was most famous for writing "The Structure of Scientific Revolutions" in 1962, which introduced the idea of "paradigm shifts" as an alternative idea to linear progression.
This is a difficult question to answer. The pure answer is no. In reality, it depends on the level of randomness in the data. If you plot the data, it will give you an idea of the randomness. Even with 10 data points, 1 or 2 outliers can significantly change the regression equation. I am not aware of a rule of thumb on the minimum number of data points. Obviously, the more the better. Also, calculate the correlation coefficient. Be sure to follow the rules of regression. See the following website: http:/www.duke.edu/~rnau/testing.htm
The central idea of a writing is the theme.
Linear. Buddhism is an example of cyclic because of the idea of rebirth.
Hammurabi was a leader so he thought of the idea for writing laws down.
Writing software is a part of developing software. The actual process of writing code can be called "writing software." "Developing software" includes includes the entire process of turning an idea into a program: everything from requirements and specifications to writing software.
I have no idea. However, in theory there is a difference.
It is possible to give an example of non-linear, but I have no idea what a non-example is. Is a non-example of linear a curve. That would be my first thought but not sure
The central idea of a writing is the theme!
Creative Writing is a genre that can fit any book, fiction nonfiction or poem. The idea of Creative Writing is creative, and has mainly an original idea for stories.
Creative Writing is a genre that can fit any book, fiction nonfiction or poem. The idea of Creative Writing is creative, and has mainly an original idea for stories.
mo idea