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Lecture25

# Lecture25 - Multiple Linear Regression Model A general...

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4/20/2011 1 Stat 350 Lecture 25 11.4 Multiple Linear Regression Model 11.5 Inferences in Multiple Regression Multiple Linear Regression Model A general additive multiple regression model: Y: dependent variable x 1 , x 2 , …, x k : predictor variables e: random deviation Normal with mean 0 and standard deviation σ independent Y 1 X 1 2 X 2 ... k X k e Multiple Linear Regression Model A general additive multiple regression model: Goal: to explain Y using the necessary predictors with the best fit Tradeoff: Want to explain the most using the least number of predictors possible. Variables can and do “overlap” Y 1 X 1 2 X 2 ... k X k e Example (#25) A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time (HOURS) to the predictors x1=distance traveled (miles) and X2= number of deliveries made. Suppose that the model equation is Y = -0.800 +0.060 x1 + 0.900x2 +e Question: What is the mean value of travel time when 3 deliveries are made and the distance is 50 miles? How to interpret β1=0.06? How to interpret β2=0.9? Example (#25) Y = total daily travel time (HOURS) X1=distance traveled (miles) X2= number of deliveries Y = -0.800 +0.060 x1 + 0.900x2 +e Question: If σ =0.5 hours, what is the probability that travel

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