The following model was fitted to observations from 1972 to...

The following model was fitted to observations from 1972 to 1979 in an attempt to explain oil-pricing behavior: $$ \hat{y}=\underset{(0.029)}{37 x_1}+\underset{(0.50)}{5.22 x_2} $$ where $\hat{y}=$ difference between price in the current year and price in the previous year, in dollars per barrel $x_1=$ difference between spot price in the current year and spot price in the previous year $x_2=$ dummy variable taking the value 1 in 1974 and 0 otherwise to represent the specific effect of the oil embargo of that year The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Interpret verbally and graphically the estimated coefficient on the dummy variable.

The following model was fitted to observations from 1972 to 1979 in an attempt to explain oil-pricing behavior:
$$
\hat{y}=\underset{(0.029)}{37 x_1}+\underset{(0.50)}{5.22 x_2}
$$
where
$\hat{y}=$ difference between price in the current year and price in the previous year, in dollars per barrel
$x_1=$ difference between spot price in the current year and spot price in the previous year
$x_2=$ dummy variable taking the value 1 in 1974 and 0 otherwise to represent the specific effect of the oil embargo of that year

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

Interpret verbally and graphically the estimated coefficient on the dummy variable.

Key Concepts

Dummy Variable in Regression

A dummy variable is used in regression analysis to represent categorical information—typically binary information such as the occurrence or non-occurrence of an event. It takes on values of 0 or 1, allowing the regression equation to adjust the predicted outcome specifically for the category or event it represents. When a dummy variable has a value of 1, the model includes the effect of that condition, and when it is 0, the effect is absent.

Interpretation of Estimated Coefficients

The estimated coefficient for a dummy variable indicates the average change in the dependent variable when the event represented by the dummy occurs (i.e., its value is 1), holding all other factors constant. This coefficient reflects an adjustment to the intercept of the regression model for the corresponding event, capturing the impact of an external intervention or a distinct period that deviates from the baseline pattern.

Graphical Representation of Dummy Variable Effects

Graphically, the effect of a dummy variable can be depicted as a vertical shift in the regression line when the dummy variable is activated (i.e., equals 1). In a plot where the dependent variable is on the vertical axis, the predicted line for the category corresponding to the event will be displaced upward or downward compared to the baseline line (where the dummy is 0). The magnitude of this shift is equal to the estimated coefficient on the dummy variable, visualizing the additional effect of the event.

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