1. What is the least-squares regression line? (A) A line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible, giving the smallest sum of the vertical distances between the observed values (y) and the predicted values (^y). (B) A line that gives the smallest total sum of squared residuals. (C) A line that makes the squares of r in the data as large as possible. (D) Both A and B. 2. What is the "squares" in a least-squares regression line equal to? (A) (observed - predicted)^2 (B) (observed - mean)^2 (C) (residuals)^2 (D) Both A and C. 3. If two variables (x and y), have a strong linear relationship and almost all of the data points fall on the least-squares regression line, then (A) x causes y to happen. (B) y causes x to happen. (C) the y-intercept should be positive. (D) there might or might not be any relationship between x and y.

1. What is the least-squares regression line? (A) A line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible, giving the smallest sum of the vertical distances between the observed values (y) and the predicted values (^y). (B) A line that gives the smallest total sum of squared residuals. (C) A line that makes the squares of r in the data as large as possible. (D) Both A and B. 2. What is the "squares" in a least-squares regression line equal to? (A) (observed - predicted)^2 (B) (observed - mean)^2 (C) (residuals)^2 (D) Both A and C. 3. If two variables (x and y), have a strong linear relationship and almost all of the data points fall on the least-squares regression line, then (A) x causes y to happen. (B) y causes x to happen. (C) the y-intercept should be positive. (D) there might or might not be any relationship between x and y.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 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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Regarding least-squares regression line.

1. What is the least-squares regression line?
(A) A line that makes the sum of the squares of the vertical distances of the data
points from the line as small as possible, giving the smallest sum of the vertical
distances between the observed values (y) and the predicted values ("y).
(B) A line that gives the smallest total sum of squared residuals.
(C) A line that makes the squares of r in the data as large as possible.
(D) Both A and B.
2. What is the "squares" in a least-squares regression line equal to?
(A) (observed - predicted)^2
(B) (observed - mean)^2
(C) (residuals)^2
(D) Both A and C.
3. If two variables (x and y), have a strong linear relationship and almost all of the data
points fall on the least-squares regression line, then
(A) x causes y to happen.
(B) y causes x to happen.
(C) the y-intercept should be positive.
(D) there might or might not be any relationship between x and y.

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