文本说明空间分析spatial regression.pptx

Regression and Spatial Regression;Regression Analysis Simple Linear Regression Model Multiple Linear Regression Model Additional Topics in Regression Analysis Spatial Regression Spatial Autoregressive Models Geographically Weighted Regression ;2;3;4;5;6;Regression Analysis Simple Linear Regression Model Multiple Linear Regression Model Additional Topics in Regression Analysis Spatial Regression Spatial Autoregressive Models Geographically Weighted Regression ;Simple Linear Regression Model Changes in Y are assumed to be caused by changes in X The relationship between X and Y is described by a linear function Linear regression population equation model： ;9;Linear Regression Model Assumptions The true relationship form is linear (Y is a linear function of X, plus random error) The error terms, εi are independent of the x values The error terms are random variables with mean 0 and constant variance, σ2 The random error terms, εi, are not correlated with one another, so that ;Ordinary Least Squares (OLS) the standard criteria for obtaining the regression line b0 and b1 are obtained by finding the values of b0 and b1 that minimize the sum of the squared differences between y and: ;Simple Linear Regression Example A real estate agent wishes to examine the relationship between the selling price of a home and its size (measured in square feet) A random sample of 10 houses is selected Dependent variable (Y) = house price in $1000s Independent variable (X) = square feet ;13;Example Here, no houses had 0 square feet, so b0 = 98.24833 just indicates that, for houses within the range of sizes observed, $98,248.33 is the portion of the house price not explained by square feet Here, b1 = .10977 tells us that the average value of a house increases by .10977($1000) = $109.77, on average, for each additional one square foot of size ;Measures of Variation Total variation is made up of two parts: ;16;Coefficient of De