ISYE6414 (Regression) Midterm 1 || Already Graded A+.
What are the variables in regression? correct answers 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? correct answers Response Variable - It varies
with changes in the predictor along with other random changes
Which regression variable is a Fixed variable? correct answers 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? correct answers 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? correct answers 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? correct answers
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? correct answers 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)
correct answers 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? correct answers 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 correct answers 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. correct answers 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. correct answers 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? correct answers 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? correct answers It means that B1 is statistically different from
zero.
What are the variables in regression? correct answers 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? correct answers Response Variable - It varies
with changes in the predictor along with other random changes
Which regression variable is a Fixed variable? correct answers 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? correct answers 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? correct answers 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? correct answers
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? correct answers 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)
correct answers 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? correct answers 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 correct answers 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. correct answers 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. correct answers 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? correct answers 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? correct answers It means that B1 is statistically different from
zero.
