ISYE 6414 - MIDTERM 1 EXAM 2024 WITH 100% ACCURATE SOLUTIONS
we do not transform - Precise Answer ✔✔If λ=1
Regression analysis is one of the simplest ways we have in statistics to investigate the relationship between two or more variables in a ___ way - Precise Answer ✔✔non-deterministic
The response variable is a ___ variable, because it varies with changes in the predicting variable, or with other changes in the environment - Precise Answer ✔✔random
The predicting variable is a ___ variable. It is set fixed, before the response is measured. - Precise Answer ✔✔fixed
regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line - Precise Answer ✔✔simple linear regression
A statistical method used to model the relationship between one dependent (or response) variable and two or more independent (or explanatory) variables by fitting a linear equation to observed data - Precise Answer ✔✔Multiple Linear Regression
a regression model which does not assume a linear relationship; a curvilinear correlation coefficient is computed (we can think of X and X-squared as two different predicting variables) - Precise Answer ✔✔polynomial regression
1) Prediction
2) Modeling
3) Testing hypothesis - Precise Answer ✔✔three objectives in regression We want to see how the response variable behaves in different settings. For example, for a different location, if we think about a geographic prediction, or in time, if we think about temporal prediction - Precise Answer ✔✔Prediction
modeling the relationship between the response variable and the explanatory variables, or predicting variables - Precise Answer ✔✔Modeling
of association relationships - Precise Answer ✔✔Testing hypotheses
We do not believe that the linear model represents a true representation of reality. Rather, we think that, perhaps, it provides a ___ - Precise Answer ✔✔useful representation of reality
intercept parameter (the value at which the line intersects the y-axis) - Precise Answer ✔✔β0
slope parameter (slope of the line we are trying to fit) - Precise Answer ✔✔β1
is the deviance of the data from the linear model - Precise Answer ✔✔epsilon (ε)
to find the line that describes a linear relationship, such that we fit this model. - Precise Answer ✔✔to find β0 and β1
pairs of data consisting of a value for the response variable,and a value for the predicting variable. And we have n such pairs - Precise Answer ✔✔simple linear regression data structure
1) identifying data structure
2) clearly stating the model assumptions - Precise Answer ✔✔modeling framework for the simple linear regression:
1) linearity
2) constant variance assumption
3) independence assumption - Precise Answer ✔✔linear regression assumptions mean zero assumption, means that the expected value of the errors is zero.
A violation of this assumption will lead to difficulties in estimating β0, and means that your model does not include a necessary systematic component. - Precise Answer ✔✔linearity assumption
which means that the variance (σ^2) of the error terms or deviances is constant for the given population. A violation of this assumption means that the estimates are not as efficient as they could be in estimating the true parameters - Precise Answer ✔✔constant variance assumption
which means that the deviances are independent random variables.
Violation of this assumption can lead to misleading assessments of the strength of the regression. - Precise Answer ✔✔Independence Assumption
errors (ε) are normally distributed. This is needed for statistical inference, for example, confidence or prediction intervals, and hypothesis testing. If this assumption is violated, hypothesis tests and confidence and prediction intervals can be misleading.v - Precise Answer ✔✔normality assumption
the variance of the error terms (σ^2) - Precise Answer ✔✔third parameter
How can we get estimates of the regression coefficients or parameters in linear
regression analysis? - Precise Answer ✔✔One approach is to minimize the sum of squared residuals or errors with respect to β0 and β1. This translated into finding the line such that the total squared deviances from the line is minimum.
to be the regression line where the parameters are replaced
by the estimated values of the parameters. - Precise Answer ✔✔fitted values
are simply the difference
between observed response and fitted values, and they are proxies of the error terms in
the regression model - Precise Answer ✔✔Residuals
The estimator for sigma square is sigma square hat, and is the
we do not transform - Precise Answer ✔✔If λ=1
Regression analysis is one of the simplest ways we have in statistics to investigate the relationship between two or more variables in a ___ way - Precise Answer ✔✔non-deterministic
The response variable is a ___ variable, because it varies with changes in the predicting variable, or with other changes in the environment - Precise Answer ✔✔random
The predicting variable is a ___ variable. It is set fixed, before the response is measured. - Precise Answer ✔✔fixed
regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line - Precise Answer ✔✔simple linear regression
A statistical method used to model the relationship between one dependent (or response) variable and two or more independent (or explanatory) variables by fitting a linear equation to observed data - Precise Answer ✔✔Multiple Linear Regression
a regression model which does not assume a linear relationship; a curvilinear correlation coefficient is computed (we can think of X and X-squared as two different predicting variables) - Precise Answer ✔✔polynomial regression
1) Prediction
2) Modeling
3) Testing hypothesis - Precise Answer ✔✔three objectives in regression We want to see how the response variable behaves in different settings. For example, for a different location, if we think about a geographic prediction, or in time, if we think about temporal prediction - Precise Answer ✔✔Prediction
modeling the relationship between the response variable and the explanatory variables, or predicting variables - Precise Answer ✔✔Modeling
of association relationships - Precise Answer ✔✔Testing hypotheses
We do not believe that the linear model represents a true representation of reality. Rather, we think that, perhaps, it provides a ___ - Precise Answer ✔✔useful representation of reality
intercept parameter (the value at which the line intersects the y-axis) - Precise Answer ✔✔β0
slope parameter (slope of the line we are trying to fit) - Precise Answer ✔✔β1
is the deviance of the data from the linear model - Precise Answer ✔✔epsilon (ε)
to find the line that describes a linear relationship, such that we fit this model. - Precise Answer ✔✔to find β0 and β1
pairs of data consisting of a value for the response variable,and a value for the predicting variable. And we have n such pairs - Precise Answer ✔✔simple linear regression data structure
1) identifying data structure
2) clearly stating the model assumptions - Precise Answer ✔✔modeling framework for the simple linear regression:
1) linearity
2) constant variance assumption
3) independence assumption - Precise Answer ✔✔linear regression assumptions mean zero assumption, means that the expected value of the errors is zero.
A violation of this assumption will lead to difficulties in estimating β0, and means that your model does not include a necessary systematic component. - Precise Answer ✔✔linearity assumption
which means that the variance (σ^2) of the error terms or deviances is constant for the given population. A violation of this assumption means that the estimates are not as efficient as they could be in estimating the true parameters - Precise Answer ✔✔constant variance assumption
which means that the deviances are independent random variables.
Violation of this assumption can lead to misleading assessments of the strength of the regression. - Precise Answer ✔✔Independence Assumption
errors (ε) are normally distributed. This is needed for statistical inference, for example, confidence or prediction intervals, and hypothesis testing. If this assumption is violated, hypothesis tests and confidence and prediction intervals can be misleading.v - Precise Answer ✔✔normality assumption
the variance of the error terms (σ^2) - Precise Answer ✔✔third parameter
How can we get estimates of the regression coefficients or parameters in linear
regression analysis? - Precise Answer ✔✔One approach is to minimize the sum of squared residuals or errors with respect to β0 and β1. This translated into finding the line such that the total squared deviances from the line is minimum.
to be the regression line where the parameters are replaced
by the estimated values of the parameters. - Precise Answer ✔✔fitted values
are simply the difference
between observed response and fitted values, and they are proxies of the error terms in
the regression model - Precise Answer ✔✔Residuals
The estimator for sigma square is sigma square hat, and is the
