multipleRegressionLab

# multipleRegressionLab - Recitation#10 and Homework#8...

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Recitation #10 and Homework #8: Multiple Linear Regression OVERVIEW This assignment is Recitation (Computer Lab) #10 as well as Homework #8. The homework assignment is to complete the 6 homework problems in this handout. You will start the homework assignment during the lab but can complete it anytime before the due date, which is Thursday, April 9 at 4pm. If you own a computer, then you can install R on it at no cost and complete the assignment at home. It is recommended that you include R output and graphs in with your home- work to help you answer the questions. 1. CASE BACKGROUND As part of a longer manufacturing process, a factory needs to cast a large number of rectangular metallic blocks. The blocks are manufactured by using a mold consisting of the main cavity, a cup through which the molten metal is poured, and two risers for cooling (see Figure 1). The size and shape of the pouring cup and risers aﬀect how quickly the metal can be poured into the mold, how quickly it cools, and whether it sets correctly. Figure 1: The mold consists of the main cavity, a pouring cup/sprue and two risers Objective: The factory needs to cast batches of 100 blocks of size 4.5 × 4.5 × 7 inches. The current casting approach is fairly conservative — it takes a long time to pour, but the blocks always set correctly and are usable. Your goal is to achieve a signiﬁcant reduction in average casting time while still ensuring that most blocks are feasible (usable). In this 1

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week’s lab, you will focus on casting time, while next week the focus will be on feasibility. In fact, the data set for use this week does not even include the variable “ Feasible ” which indicates whether a casting is usable. Variables: The following variables can be varied: Riser Height, Riser Diameter, Riser 1 Position, Riser 2 Position, Gate Diameter, Cup Height, Sprue Height, Sprue Diameter Bottom, and Sprue Diameter Top (see Figure 1). The response variable is “ BatchTime ”. Figure 2: Parameters for the mold construction Data: To obtain data on how various variable values aﬀect pouring and cooling, a batch of 100 castings is poured with random variations in the mold variables about their baseline values. The data are available in the ﬁle castdata.csv . Each row contains parameter values (the inputs), and the cast batch time. The ﬁrst line in the ﬁle contains the header with the names of the variables. The data start in the second row. The ﬁrst row of data has the baseline values, that is, the values of the variables used in the current casting approach. . 2. ASSIGNMENT This lab project will guide you through the analysis. Importing data into R: First import the data into R, using the following commands: setwd("C:/DataDirectory") cast <- read.csv("castdata.csv",header=TRUE) where DataDirectory is the directory in which the data are stored. If you store your data in a ﬂashdrive your directory might start with a diﬀerent letter such as H: \ or F: \ . You can
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multipleRegressionLab - Recitation#10 and Homework#8...

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