Stat1250_SGTA10

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Macquarie University *

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1250

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Statistics

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Apr 3, 2024

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docx

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4

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© Copyright Macquarie University 1 Stat1250 SGTA 10: Linear Regression You are expected to read this material and think about the problems before attempting to solve them. SGTA 10: Linear Regression In this SGTA we will: Discuss scatter plots showing relationship between 2 numerical variables. Use regression analysis to investigate the relationship between two numerical variables. The principle of regression analysis was described and explained by Francis Galton in the 1870s and 1880s. Initially he investigated geniuses in various fields and noted that their children, while typically gifted, were almost always closer to the average than their exceptional parents. He later described the same effect numerically by comparing fathers’ heights to their sons’ heights. Again a son’s height was typically closer to the average than the height of his father. Galton hypothesised that the taller the father the taller the son would be. He plotted heights of fathers and heights of their sons for a number of father- son pairs, then attempted to fit a straight line through the data. Galton used the equation of the line to predict a son’s adult height based on the height of his father. Figure 1: Sir Francis Galton; Wikipedia (Public domain image)
© Copyright Macquarie University 2 Stat1250 SGTA 10: Linear Regression Scatter plots 1. Draw a curve that might depict the relation between the following variables. (Note: use the first variable given as the independent variable.) a. Maximum daily temperature and soft drink sales of a retailer. b. Odometer reading and sale price of a used car. c. Annual income and credit card balance of bank clients. a. b. c. 2. Consider the four scatter plots below. For each plot, with your group, discuss any relation that you can see between the variables.
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