1. summarize data with a simple expression, 2. predict values of y for other, ex
ID: 3177061 • Letter: 1
Question
1. summarize data with a simple expression,
2. predict values of y for other, experimentally untried values of x,
3. handle data analytically
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The answer in the book didn't go into much detail
Least squares and regression lines When we try to fit a line y = mx + b to a set of numerical data points (x_2, y_2), ..., (x_n, y_n), we usually choose the line that minimizes the sum of the squares of the vertical distances from the points to the line. In theory, this means finding the values of m and b that minimize the value of the function w = (mx_1 + b - y_1)^2 + + (m x_n + b - y_n)^2. (See the accompanying figure.) Show that the values of m and b that do this are m = (sigma x_k) (sigma y_k) - n sigma x_k y_k/(sigma x_k)^2 - n sigmax_k^2, b = 1/n (sigma y_k - m sigma x_k), with all sums running from k = 1 to k = n. Many scientific calculators have these formulas built in. enabling you to find m and b with only a few keystrokes after you have entered the data. The line y = mx + b determined by these values of m and b is called the least squares line, regression line, or trend line for the data under study. Finding a least squares line lets you summarize data with a simple expression, predict values of y for other, experimentally untried values of x, handle data analytically. We demonstrated these ideas with a variety of applications in Section 1.4. In Exercises 66-68, use Equations (2) and (3) to find the least squares line for each set of data points. Then use the linear equation you obtain to predict the value of y that would correspond to x = 4.Explanation / Answer
The least square line or regession lines.
1. Summarize the data with simple expression: It means using least square line one can plot the data in such a way that sum of squared deviances of all data points from fitted line is minimum. It shows all data points gathered in one fitted line. It gives the y-intercept where line cuts the y-axis. It also gives the slope of the line which represent the relation beween X and Y, whether it is positive or negative.
2. Predict values of y for another, experimentally untried values of x:
The fitted regression line is oftained from given data points. One can use this fitted line to predict the values of responce variable Y for other values of X which are not used in fitting the line. The regression line given the relation between X and Y hence value of X can be used to find the value of Y.
3. Handle data analytically.: Regression analysis uses the testing best fit of line for given data. If the fitted line is not best fit for given data then another model is fitted to the given data by doing some changes in independent variables or removing some indepenent variables. Also significance of each regressor is also tested while fitting the regression line. It also given the R2 value , coefficient of determination which represents the % of variation in responce variables by regressor ariable for fitted line.
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