Describe the number of points that simultaneously lie in each of the three planes shown in each part of Figure 1.2.

Linear Regression Mathematical Models Expression that describes the relationship between variables 2 types o Deterministic model o Probabilistic model Hypothesize 2 components Deterministic Random error Straight line probabilistic model y = 0+ x1+ y dependent variable x independent variable E(y) = 0 + 1x Deterministic component (epsilon) Random error component 0(beta zero) = yintercept of the line 1(beta one) = slope of the line How do you determine what line “fits best” on a Scattergram Least Squares line Sum of the errors = 0 o Mean error = 0 Sum of squared errors (SSE) is smaller than for any other straightline model o Error variance is minimum How to determine the line: Finding it on the Calculator: Input the data given (STAT, Edit) Finding line STAT, CALC, LinReg LinReg will automatically have L1 as the x values and L2 as the y values Example You’re a marketing analyst for Hasbro Toys. You gather the following data: Ad Expenditure (100$) Sales (Units) 1 1 2 1 3 2 4 2 5 4 Find the least squares line relating sales and advertising. Basic Assumptions of Probability Distribution: