Linear Regression Linear regression is an approach to modeling the relationship

Question

Linear Regression Linear regression is an approach to modeling the relationship between two quan- tities with a linear function. The linear function obtained from linear regression is a line with the property that the sum of the squares of the errors is minimal. For this project, we will consider the error between a data value (ri,y) and the value from the linear model f mr b to be Note that linear function f(z) ma b is completely determined by the values m (ts slope) and b (its vertical intercept). Thus m and b must be computed in such a way that the sum of the squares of the errors is minimal. In other words, we wish to minimize The n here represents the number of data values We can think of the m and b as the variables in the equation above, as we would pr the values of r, and (these would be data values that collect the this in mind, we can determine m and b that makes S b) minimal by using calculus. It turns out that the optimal values of m and b are Using methods discussed in class, show that the m and b given above are the critical points of b). Then show that this is indeed where the minimum of S occurs. Then find a linear regression for the following collection of points: 11,23 T, 14.23) (9, 17.5 8) (2, 4.1 Make sure to explain why your m and b values are indeed where S(m,b) is minimal by including a brief discussion about discriminant and second partials Remark. In mathematics, it is sometimes useful to introduce constants to re- place more complicated looking expressions. For example, we know that the

Explanation / Answer

Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous variables. Or we can say that linear regression is a statistical procedure for prediction the values of a dependent variable from an independent variable when the relationship between the variables is linear. The variable denoted by x, is the predictor, explanatory, or independent variable and the other variable y is the response, outcome or dependent variable. If the independent variable is a vector then the model is multiple linear regression model.

The method given in the question is fitting of the regression model using ordinary least squares. The formulas for slope m and intercept is given. using that we can estimate y values and the resulting equation is often referred to as the least squares regression line or least squares line or estimated regression equation. Using this model we can predict the future values also.

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