ISYE 6414 (REGRESSION) MIDTERM EXAM |ACCURATE ANSWERS |VERIFIED
What are the variables in regression? - ACCURATE ANSWER1. Response (dependent) variable - one particular variable that we are interested in understanding or modelling, such as sales of a particular product.
2. Predicting or Expla...
ISYE 6414 (REGRESSION)
MIDTERM EXAM |ACCURATE
ANSWERS |VERIFIED
What are the variables in regression? - ACCURATE ANSWER✅✅1. Response
(dependent) variable - one particular variable that we are interested in
understanding or modelling, such as sales of a particular product.
2. Predicting or Explanatory (independent) variable - set of other variables that we
think might be useful in predicting or modelling the response variable (like the
price of a product)
Which regression variable is a Random variable? - ACCURATE
ANSWER✅✅Response Variable - It varies with changes in the predictor along
with other random changes
Which regression variable is a Fixed variable? - ACCURATE
ANSWER✅✅Predicting Variable - It does not change with the response but it is
set fixed before the response is measured.
What are the objectives in regression analysis? - ACCURATE ANSWER✅✅1.
Prediction - of the response variable
2. Modelling - the relationship between the response variable and the explanatory
variables
3. Testing - hypotheses of association relationships.
What are the given assumptions when building a linear regression model? -
ACCURATE ANSWER✅✅1. Linearity/Mean Zero Assumption - it cannot be true
,that for certain subgroups in the population, the model is consistently too low,
while for others, it's consistently too high.
2. Constant Variance Assumption - means that it cannot be true that the model is
more accurate for some parts of the population, and less accurate for other parts of
the populations.
3. Independence Assumption are independent random variables - it cannot be true
knowing that the model under-predicts y for one particular case tells you anything
or all about what it does for any other case. (her language)
4. Normally distributed.
What is the value that is being optimized towards in a linear regression problem? -
ACCURATE ANSWER✅✅Minimizing the sum of squared errors
In terms of model parameter interpretation, how would you interpret a positive
value for B1, negative value, and value close to 0? - ACCURATE ANSWER✅✅A
positive value of B1 is consistent with a direct relationship between x and y
A negative value of B1 is consistent with an inverse relationship between x and y
A close to zero value of B1 means that there is not a significant association
between x and y
What are the interpretations of the Least Squares estimated coefficients (B hat 1
and B hat 0) - ACCURATE ANSWER✅✅B hat 1 is the estimated expected
change in the response variable associated with the unit of change in the predicting
variable
,B hat 0 is the estimated expected value of the response variable when the
predicting variable equals zero
What is extrapolation? - ACCURATE ANSWER✅✅When you try to predict a
value using your regression model that is outside of the observed range. It is
unreliable to use extrapolation.
Assuming that the data are normally distributed, under the simple linear model, the
estimated variance has the following sample distribution:
A) Chi-square with n-2 degrees of freedom
B) T-distribution with n-2 degrees of freedom
C) Chi-square with n degrees of freedom
D) T-distribution with n degrees of freedom - ACCURATE ANSWER✅✅A) Chi-
square with n-2 degrees of freedom
The fitted values are defined as:
A) The difference between observed and expected responses
B) The regression line with parameters replaced with the estimated regression
coefficients
C) The regression line
D) The response values. - ACCURATE ANSWER✅✅B) The regression line with
parameters replaced with the estimated regression coefficients.
The estimators of the linear regression model are derived by:
, A) Minimizing the sum of squared differences between observed and expected
values of the response variable.
B) Maximizing the sum of squared differences between observed and expected
values of the response variable.
C) Minimizing the sum of absolute differences between observed and expected
values of the response variable.
D) Maximizing the sum of absolute differences between observed and expected
values of the response variable. - ACCURATE ANSWER✅✅A) Minimizing the
sum of squared differences between observed and expected values of the response
variable.
When using the t-test for statistical significance, when would you interpret B1 as
statistically significant? - ACCURATE ANSWER✅✅We reject the null
hypothesis of the absolute value of the t-value is large. If the null hypothesis is
rejected, we interpret this as B1 being statistically significant.
What is statistical significance? - ACCURATE ANSWER✅✅It means that B1 is
statistically different from zero.
When using the p-value test for statistical significance, when would you interpret
B1 as statistically significant? - ACCURATE ANSWER✅✅If the P-value is small
(<.01) then we would reject the null hypothesis and determine that B1 is
statistically significant.
What is the p-value? - ACCURATE ANSWER✅✅The p-value is a measure of
how reject-able the null hypothesis is. The smaller the p-value, the more reject-able
the null hypothesis is for the observed data.
The estimators for the regression coefficients are:
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