Simple linear regression Model 简单线性回归模型 Relationship between Variables Is a Linear Function The Straight Line that Best Fit the Data Y intercept Random Error Yi=Bo+B,Xi+8 Dependent (Response) Independent Slope Variable (Explanatory) Variable
Simple Linear Regression Model 简单线性回归模型 Yi Xi i = + + 0 1 Y intercept Slope • The Straight Line that Best Fit the Data • Relationship Between Variables Is a Linear Function Random Error Dependent (Response) Variable Independent (Explanatory) Variable
Population Linear regression Model Y=阝0+β1X1+ i Observed Value 8,=Random Error 阝0+β1X X Observed Value
i = Random Error Y X Population Linear Regression Model Observed Value Observed Value YX = 0 + 1Xi Yi = + Xi + i 0 1
Sample linear regression model 简单线性相关模型 bo+bX Predicted Value of y for observation i X = Value of X for observation i bo =Sample y-intercept used as estimate of the population Bo b,=Sample Slope used as estimate of the population BI
Sample Linear Regression Model 简单线性相关模型 Y i = b 0 + b 1 X i Yi = Predicted Value of Y for observation i Xi = Value of X for observation i b0 = Sample Y - intercept used as estimate of the population 0 b1 = Sample Slope used as estimate of the population 1
Simple Linear regression Equation: Example Annual Store Square Sales Feet ($000) ou wish to exarate 1726 3.681 relationship bet eesthe 1,542 3.395 square Footage o 3 2,816 6.653 produce stores and its 5555 9,543 annual sales. Sample 5 1.292 data for 7 stores were 3,318 obtained. Find the 6 2,208 5563 equation of the straight 7 1.313 3,760 line that fits the data best
Simple Linear Regression Equation: Example You wish to examine the relationship between the square footage of produce stores and its annual sales. Sample data for 7 stores were obtained. Find the equation of the straight line that fits the data best Annual Store Square Sales Feet ($000) 1 1,726 3,681 2 1,542 3,395 3 2,816 6,653 4 5,555 9,543 5 1,292 3,318 6 2,208 5,563 7 1,313 3,760
Scatter Diagram Example 12000 10000 8000 s6000 4000 2000 0 100020003000400050006000 square Feet
Scatter Diagram Example 0 2000 4000 6000 8000 10000 12000 0 1000 2000 3000 4000 5000 6000 S q u a re F e e t Annual Sales ($000)