Patrick Power PRO
Economics PhD @ Boston University
Extra Bits and Bytes for Regression
Business Analytics
Interpreting Coefficients
I think it's important to keep in mind that we are fitting a linear model to data without assuming the the Conditional Expectation Function is linear
Y_i = \beta_0 + \beta_1X_i + \varepsilon_i
Linear Regression Model
The average value of Y when X is zero
Interpretation
The predicted value of Y when X is zero
More Precise Interpretation
Y_i = \beta_0 + \beta_1X_i + \varepsilon_i
Linear Regression Model
The average change in Y when X increases by one-unit
Interpretation
The predicted change in Y when X increase by one Unit
More Precise Interpretation
In the following linear regression model, what does
\beta_0, \beta_1
(A)
(B)
capture, respectively?
\text{Price}_i = \beta_0 + \beta_1 \text{Size}_i + \varepsilon_i
The average price of a house, The average change in price when the size of the house increases by one unit
The average price of a house when size is zero, the average change in price when the size of the house increases by one unit
(C)
The fixed cost of a house, the marginal cost of the house
The average price of a house when size is zero, the average effect of increasing the size of the house by one unit
(D)
Y_i = \beta_0 + \beta_1X_{1i} + \beta_2X_{2i}+ \varepsilon_i
Linear Regression Model
The average change in Y when X1 increases by one-unit holding X2 Constant
Interpretation
The predicted change in Y when X1 increase by one unit holding X2 constant
More Precise Interpretation
In the following linear regression model, what does
\beta_0, \beta_1
(A)
capture, respectively?
\text{Price}_i = \beta_0 + \beta_1 \text{Size}_i + \beta_2\text{Beacon}_i + \varepsilon_i
The average price of a house when Beacon is zero, The average change in price when the size of the house increases by one unit holding Beacon constant
The Fixed Cost, the Marginal Cost
(B)
(D)
The average price of a house when Size is zero, The average change in price when the size of the house increases by one unit holding Beacon constant
(C)
The average price of a house when Size and Beacon is zero, The average change in price when the size of the house increases by one unit holding Beacon constant
Y_i = \beta_0 + \beta_1X_{i} + \varepsilon_i
Linear Regression Model with a Dummy Variable
The average value of Y when X is zero
Interpretation
The difference in Average Value of Y when X is 0 and when X is 1
Interpretation
X_i \in \{0, 1\}
Dummy Variable
In the following linear regression model, what does
\beta_2
capture
\text{Price}_i = \beta_0 + \beta_1 \text{Size}_i + \beta_2\text{Beacon}_i + \varepsilon_i
In the following linear regression model, what does
\beta_3
(A)
(B)
capture?
\text{Price}_i = \beta_0 + \beta_1\text{Size}_i + \beta_2 \text{Beacon}_i + \beta_3\text{Size}_i \times \text{Beacon}_i + \beta_4 \text{garage}_i + \varepsilon_i
The effect of increasing the size of a house by one unit on the price of the house
(C)
The difference between Beacon and non-Beacon areas in the average change in Price associated with a one-unit increase in Size holding Garage constant
The average change in Price when increasing Size by one unit holding Beacon and Garage constant
In the following linear regression model, what does
\beta_0
(A)
(B)
capture?
\text{Price}_i = \beta_0 + \text{C(BuildingStyle)}_i + \varepsilon_i
The average price of a house
(C)
The average price of a house in the reference/default category of buildingStyle
The average price of a house with no building style
More Questions
linear_model = smf.ols('price ~ size + beacon', data=df)Which linear regression equation corresponds to the following line of code?
(A)
(B)
(C)
\text{Size}_i = \beta_0 + \beta_1\text{Price}_i + \text{Beacon}_i + \varepsilon_i
\text{Price}_i = \beta_1\text{Size}_i + \beta_2\text{Beacon}_i + \varepsilon_i
\text{Price}_i = \beta_0 + \beta_1\text{Size}_i + \beta_2\text{Beacon}_i
(D)
\text{Price}_i = \beta_0 + \beta_1\text{Size}_i + \beta_2\text{Beacon}_i + \varepsilon_i
\text{Price}_i = \beta_0 + \beta_1\text{Size}_i + \beta_2\text{Size}^2_i + \varepsilon_i
What is the best interpretation of
\beta_2
in the following Quadratic Regression?
(A)
(B)
(C)
(D)
The average change in price when increasing size by one unit
We cannot include higher order terms in a linear regression model
The average change in price when increasing the squared size by one unit, holding the size constant
Captures how the marginal change in price with respect to size varies as we increase size
More Questions
Which linear model will have the lowest Mean Squared Error?
(A)
linear_modelA = smf.ols('price ~ size + I(size **2)', data=df)(B)
linear_modelB = smf.ols('price ~ size + I(size **2) + I(size**3)', data=df)(C)
linear_modelC = smf.ols('price ~ size', data=df)True or False
(A)
(B)
True
False
A low
is indicative of selection bias
R^2
Extra Bits and Bytes for Regression
By Patrick Power
Extra Bits and Bytes for Regression
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