A3 Linear regression.docx

A3 Linear regression.docx - Question 1(50 points Objectives...

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Question 1 (50 points) Objectives of the assignment: Find a regression line and plot it on the scatterplot. Examine the effect of outliers on the regression line. Use the regression line to make predictions and evaluate how reliable these predictions are. Modern Olympic Games have changed dramatically since their inception in 1896. For example, many commentators have remarked on the change in the quality of athletic performances from year to year. Regression will allow us to investigate the change in winning times for one event— the 1,500-meter race. Instructions: Our dataset contains the following variables: Year: the year of the Olympic Games, from 1896 to 2000. Time: the winning time for the 1,500-meter race, in seconds. First, explore the relationship between the two quantitative variables— year and time . Produce a scatterplot and use it to verify that year and time are nearly linear in their relationship. Here's a reminder of how to do this in Excel: Select all the data in columns A and B, and then choose Scatter in the Charts group on the Insert tab. Choose the first scatterplot option (Scatter with only Markers). Now we have a scatterplot, but the data is all towards the top of the plot. To fix this: Right-click on the Y axis and choose Format Axis from the pop-up menu. Make sure that Axis Options is selected on the left, and then next to Minimum enter 200 in the textbox. Click Close. Observe that the form of the relationship between the 1,500-meter race’s winning time and the year is linear. The least squares regression line is therefore an appropriate way to summarize the relationship and examine the change in winning times over the course of the last century. Next find the least squares regression line and plot it on a scatterplot. To do that in Excel: Right-click on one of the points in the graph and choose Add Trendline from the pop-up menu. Make sure that Trendline Options is selected on the left, and then check the boxes next to Display Equation on chart and Display R-squared value on chart. Click Close. (You should see a graph window with the scatterplot and the regression line plotted on it. The regression line equation appears on the graph next to the line itself.)
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Question 1: (25 Points) Give the equation for the least squares regression line and interpret it in context (What is the result saying). Question 2: (25 Points) Our least squares regression line associates years as an explanatory variable, with times in the 1,500-meter race as the response variable. Use the least squares regression line you found in question 1 to predict the 1,500-meter time in the 2008 Olympic Games in Beijing.
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Question 2 (Part 1 25 Points) Linear regression is a method of estimating the portion of a cost that is variable and the portion that is fixed. This method models the relationship between an activity and the total cost by fitting a linear equation to the data. Unlike the high-low method which uses only two data points, linear regression uses all data points in constructing the cost equation, making it much superior to the high-low method. A linear regression generates information for a cost equation
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