Answered: The least squares technique minimizes…

The least squares technique minimizes the sum of the squares of the vertical distances between the actual y values and the predicted values of y True or false

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 21CM

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Concept explainers

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 predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

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The least squares technique minimizes the sum of the squares of the vertical distances between the actual y values and the predicted values of y True or false

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The least squares line ŷ =10 + 5x describes the following coordinates: (1, 15), (2, 20), (3, 25), and (4, 30). Using these data as a specific example, explain the meaning of "least squares." The line ŷ = 10 + 5x minimizes the sum of the squared horizontal distances from the points to the line. The line ŷ = 10 + 5x minimizes the sum of the squared difference between the x and y values. The line ŷ = 10 + 5x minimizes the sum of the vertical distances from the points to the line. The line ŷ = 10 + 5x minimizes the square of the standard deviation. The line ŷ = 10 + 5x minimizes the sum of the squared vertical distances from the points to the line.
Suppose that you have the following points (1,10), (3,8) (5,7) ( 7,6) and ( 4.4). Write the equation of the least squares line that best fits the data. Find r and r2 for the data given
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The residual plot shows the residuals for the least- squares line relating price of a used car (y) to the number of miles driven (x). Residuals Residual Plot for Miles Driven vs Price 10,000 5,000 -5,000 50,000 100,000 150,000 200,000 Number of Miles Driven Based on the residual plot, is the linear model appropriate for the relationship between miles and price? No, because there are clear outliers in the residual plot. No, because there is a clear curved pattern in the residual plot. No, because there does not appear to be a pattern to the residuals. Yes, because there is a clear curved pattern in the residual plot. Yes, because there does not appear to be a pattern to the residuals.