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What are the assumptions for multiple linear regression? correct answers Linearity/Mean zero assumption, Constant Variance, Independence and Normality (for statistical inference) what are the model parameters to be estimated in MLR? correct answers B0 (intercept), B1-Bp, and sigma squared In ...

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  • August 20, 2024
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ISYE 6414 - Unit 2 || A+ Verified Solutions.
What are the assumptions for multiple linear regression? correct answers Linearity/Mean zero
assumption, Constant Variance, Independence and Normality (for statistical inference)

what are the model parameters to be estimated in MLR? correct answers B0 (intercept), B1-Bp,
and sigma squared

In multiple linear regression, the model can be written in...? correct answers Matrix form.

design matrix correct answers a matrix consisting of columns of predicting variables including
the column of ones corresponding to the intercept:

simple linear regression correct answers linear regression with one quantitative predicting
variable

ANOVA correct answers linear regression with one or more qualitative predicting variables

Multiple linear regression correct answers multiple quantitative and qualitative predicting
variables

in MLR, the sampling distribution for sigma^2 is MSE ..... correct answers chi-square with n-p-1
DF

marginal model (SLR) correct answers captures the association of one predicting variable to the
response variable marginally, that means without consideration of other factors.

conditional model (MLR) correct answers captures the association of a predictor variable to the
response variable, conditional of other predicting variables in the model.

We can make causality statements for... correct answers experimental designs

We can make associated statements for... correct answers observational studies

3 ways Predicting Variables can be distinguished as: correct answers Controlling, Explanatory,
Predictive

Controlling factors correct answers to control for bias selection in the sample. They are used as
'default' variables in order to capture more meaningful relationships.

Explanatory factors correct answers to explain variability in the response variable; they may be
included in the model even if other "similar" variables are in the model

Predictive factors correct answers to best predict variability in the response regardless of their
explanatory power

, The objective of multiple linear regression is:

A) To predict future new responses
B) To model the association of explanatory variables to a response variable accounting for
controlling factors.
C) To test hypotheses using statistical inference on the model.
D) All of the above. correct answers D

2. Which is correct?

A) A multiple linear regression model with p predicting variables but no intercept has p model
parameters.
B) The interpretation of the regression coefficients is the same whether or not interaction terms
are included in the model.
C) Multiple linear regression is a general model encompassing both ANOVA and simple linear
regression.
D) None of the above. correct answers C

Which is correct?

A) The regression coefficients can be estimated only if the predicting variables are not linearly
dependent.
B) The estimated regression coefficient beta hat i is interpreted as the change in the response
variable associated with one unit of change in the i-th predicting variable.
C) The estimated regression coefficients will be the same under marginal and conditional model;
only their interpretation is not.
D) Causality is the same as association in interpreting the relationship between the response and
predicting variables. correct answers A

Which one correctly characterizes the sampling distribution of the estimated variance?

A) The estimated variance of the error term has a chi-squared distribution regardless of the
distribution assumption of the error terms.
B) The number of degrees of freedom for the chi-squared distribution of the estimated variance
is n - p - 1 for a model without an intercept.
C) The sampling distribution of the mean squared error is different of that of the estimated
variance.
D) None of the above. correct answers D

What is B^ in MLR? correct answers a linear combination of Y's and is normally distributed.

σ^2 hat distribution is? correct answers chi-square, n-p-1 DF

What is the sampling distribution for individual β hat? correct answers t-distribution with n-p-1
DF

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