PracWeek8 - Complete

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May 31, 2024

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Linear Regression – Part 1 Employability Skills As you complete this exercise, think about which of these employability skills you are using: What will we cover in this Practical? In this practical exercise we will: Create scatterplots. Fit a least squares regression line. Saving your work Don’t forget that it is useful to save your work. Save your work to your storage device to retain a copy. In this practical exercise, we use a data set collected on people living in Peru. Anthropologists gathered these data to determine the long-term effects of a change in environment on blood pressure. The data were collected from people who migrated from a primitive culture, high in the Andes, to mainstream Peruvian society - at a much lower altitude. Open the Peru.xlsx data file from iLearn. The variables in the Peru Data worksheet are described below. Column Variable Name Description ___________________________________ A AGE Age in years B YEARS Years since migration C WEIGHT Weight in kilograms D HEIGHT Height in millimetres E CHIN Chin skin fold thickness in millimetres F FOREARM Forearm skin fold thickness in millimetres 1 | Linear Regression – Part 1 Copyright Macquarie University 2020 Download and open the Peru data The Peru data

G CALF Calf skin fold thickness in millimetres H PULSE Pulse rate in beats per minute I DIASTOL Diastolic blood pressure J BMI Body mass index We will use Excel to examine the relationship between some of the variables in the Peru data set. Because interest was primarily in whether or not there is a relationship between systolic blood pressure (SYSTOL) and years since migration (YEARS) let’s begin by creating a scatterplot of this relationship. We will use YEARS as the predictor variable on the x axis and SYSTOL as the response variable on the y axis. To create a scatterplot, recall that we: Select the columns of data to be displayed in the scatterplot. Select Insert from the main menu bar. Select a Scatter plot from the Charts menu or choose the Scatter plot from the Recommended Charts. Add a Title to the scatterplot and Axis Titles. Sketch the scatterplot in the space below. Do you think that there is a positive, negative or no relation between systolic blood pressure and the number of years since migration ? There appears to be no relation. The data is scattered around a fairly flat line. 2 | Linear Regression – Part 1 Copyright Macquarie University 2020 K SYSTOL Systolic blood presure Relations between two numerical variables 80 90 100 110 120 130 140 150 160 170 180 0 10 20 30 40 50 Systolic Blood Presssure Years Since Migration Systolic Blood Pressure vs Years Since Migration

Now make scatterplots examining the relationships between systolic blood pressure and chin skin fold thickness , and systolic blood pressure and weight . For each scatterplot, SYSTOL should be the response variable on the y axis. Each of CHIN and WEIGHT will be the predictor variable for each of the scatterplots. You can use the Formal Axis command to allow the relation in the data to be more easily seen. To do this, select the x or y axis for a scatterplot. Right click and use the Format Axis command to change the minimum value for that axis to a suitable value. For example, for the variable SYSTOL on the y axis, the value of 80 could be used for the lower bound. Describe the relations you see in the table below. Peru: Relationship SYSTOL and YEARS There appears to be no relation. The data is scattered around a fairly flat line. SYSTOL and CHIN There appears to be no relation. The data is scattered around a fairly flat line. SYSTOL and WEIGHT There appears to be a positive linear relation between SYSTOL and WEIGHT. Now for each of these variables we are going to perform a linear regression to determine whether or not there is a linear relationship between each variable and systolic blood pressure. Linear regression: SYSTOL vs YEARS We will fit a linear model to these data and obtain appropriate plots to check assumptions. Click on Data then click on Data Analysis . In the Window that pops up select Regression then click OK. Select the SYSTOL data as Input Y Range and the YEARS data as Input X Range . Select Labels if you are also highlighting the column labels . Select Residuals and Residual Plots . Select New Worksheet Ply: Click OK . From the Residual Output (contained in the Summary Output created by Excel) construct a histogram of the residuals using the default bins. Excel shows the results of the regression analysis but we need to examine the assumptions for the hypothesis test to ensure that it is valid to conduct the linear regression. Our assumption checks are listed in the table on the next page. Fill in the table to determine whether or not the assumptions are met: Linear regression assumptions 3 | Linear Regression – Part 1 Copyright Macquarie University 2020

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