12. Regression

Linear Regression & Least Squares Method

Multiple Choice
In simple linear regression, the least squares regression line is defined as the line that minimizes the sum of the squared what?
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Multiple Choice
In regression analysis, which method is commonly used to estimate the parameters of a linear model by minimizing the sum of the squared differences between observed and predicted values? $min (\sum_{i = 1}^{n} {(y_{i} - ŷ_{i})}^{2})$
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Multiple Choice
Which of the following is not one of the purposes of a line of regression in linear regression using the least squares method ( $least squares$ )?
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Multiple Choice
In linear regression using the least squares method, which expression can be simplified to find the slope of the trend line in the scatterplot?
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Multiple Choice
In linear regression using the least squares method, which of the following equations best approximates the line of best fit for a set of data points $(x, y)$ ?
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Multiple Choice
In simple linear regression with one predictor $x$ , what is the equation of the least squares regression line used to predict $y$ from $x$ ?
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Multiple Choice
Given the least squares regression equation $y = a + b x$ , what does the coefficient $b$ represent?
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Multiple Choice
In linear regression using the least squares method, the line of best fit for a scatterplot always passes through which pair of points?
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Multiple Choice
In linear regression using the least squares method, which formula correctly represents the slope of the line of best fit for a set of data points $(x, y)$ ?
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Multiple Choice
In simple linear regression, what does the graph of the regression model typically show?
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Multiple Choice
In linear regression using the least squares method, what is the expected shape or equation of the calibration plot relating the dependent variable to the independent variable?
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Multiple Choice
In linear regression, the least squares method minimizes which of the following quantities?
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Multiple Choice
In a regression analysis using the least squares method, what is the primary objective when fitting a line to the data?
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Textbook Question
[DATA] Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL levels. He obtained the following data.
b. Determine the least-squares regression equation from the sample data.
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Multiple Choice
Given a set of data points, the least squares regression line is calculated to best fit the data. Which of the following values is the most likely approximate slope of the line of best fit if the data shows a strong negative linear relationship?
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