Explanation Justification: Residual: The residual corresponding to a predictor variable is given as the difference between the actual value of the response variable and the predicted value. That is, e = y − y ^ , where y is the actual value of the response variable and y ^ is the predicted value of the response variable for same predictor variable. Leverage: An observation, whose predictor variables values ( x values) are far from the mean of the predictor variables values ( x values) is known as leverage point. Leverage point pulls the regression line to it and has a large effect on the regression line

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Chapter 8.3, Problem 3JC

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Explain whether the point in the scatterplot is a high leverage point, a large residual or an influential point.

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Chapter 8.3, Problem 2JC

Chapter 8.7, Problem 4JC

Chapter 8 Solutions

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

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Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY

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Explain whether the point in the scatterplot is a high leverage point, a large residual or an influential point.

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Explain whether the point in the scatterplot is a high leverage point, a large residual or an influential point.

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Chapter 8 Solutions