Simple linear regression statstutor（简单线性回归statstutor）.pdfVIP

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between the two variables. Straight line formula Central to simple linear regression is the formula for a straight line that is most commonly represented as y mx c or y a bx . Statisticians however generally prefer to use the following form involving betas: y   x 0 1 The variables y and x are those whose relationship we are studying. We give them the following names:  y : dependent (or response) variable;  x : independent (or predictor or explanatory) variable. It is convention when plotting data to put the dependent and independent data on the y and x axis respectively; 0 and 1 are constants and are parameters (or coefficients) that need to be estimated from data. Their roles in the straight line formula are as follows:  0 : intercept;  1 : gradient. For instance the line y 10.5x has an intercept of 1 and a gradient of 0.5. Its graph is as follows: Model assumptions In simple linear regression we aim to predict the response for the ith individual, Yi , using the individual‟s score of a single predictor variable, X i . The form of the model is given by: Y   X  i 0 1 i i which comprises a deterministic component involving the two regression coefficients ( 0 and 1 ) and a random component involving the residual (error) term ( i ). The deterministic component is in the form of a straight line which provides the predicted (mean/expected) response for a given predicto