Yannick Kurvers, 8008701
3a)
βdurset = 0.17. Given that neither the target variable (selling price) or this predictor variable
have been transformed, this coefficient can be interpreted as the amount of euros that the selling price
increases with, when the duration increases with 1 day (and all other variables are held equal). As this
was modelled with a linear regression, an assumption is that the effect of durset on eprice is linear.
This could be violated if the relationship is not linear. For example, it could be the case that
eprice indeed increases as durset increases, but that this effect slows down at around 5 days, and
then starts to approach some limit. This could happen if a longer duration initially allows more potential
buyers to see the product and thus allows for a greater number of bids. However, after some days
most potential bidders have seen the product, and longer durations do not increase the price by a
meaningful amount anymore. This would be a logarithmic relationship
3b)
While both the median spline and the fitted values follow a similar trajectory across all values
of durset, the median spline does slightly deviate from the linear fit.
The median spline is not perfectly straight, but shows a subtle deviation that suggests there
could be some curvature in the relationship between durset and eprice. The median spline starts with
a slight upward bend and is followed by a potential flattening and/or dip at the higher values of durset,
possibly suggesting an inversely U-shaped curvature.
4a)
Adding a second-degree polynomial term (durset2) to the semilog model allows us to capture a
more complex relationship between auction duration (durset) and the final price (eprice). This
approach goes beyond the assumption of linearity and tests for an inverted u-shaped relationship,
where there is an optimal auction duration that maximizes the final price.
From the model, the coefficient of durset is 0.50, indicating that initially, each additional auction
day increases the price. However, the coefficient of durset 2 is -0.05, which is negative and significant.
This suggests that after a certain point, the effect of longer auction durations becomes negative,
leading to a decline in the final price.
These coefficients together confirm an inverted u-shape: prices rise with increasing auction
duration, reach a peak, and then begin to fall. This aligns with expectations—short auctions may not
attract enough bidders, while overly long auctions may cause buyers to lose interest or reduce
competition.
The presence of a significant negative durset2 term helps pinpoint the optimal auction duration.
At this duration, sellers achieve the highest price on average.
4b)
To determine the value of durset at which sellers achieve the maximum price (eprice), we
need to find the peak of the polynomial function y = a + bx + cx 2. This involves calculating the point
where the first derivative equals zero, as this indicates the maximum of the curve.
To Find the Maximum:
The polynomial function is:
y=a+b⋅x+c⋅x2
To find the peak, take the derivative and set it equal to zero:
dydx=b+2c⋅x
1
3a)
βdurset = 0.17. Given that neither the target variable (selling price) or this predictor variable
have been transformed, this coefficient can be interpreted as the amount of euros that the selling price
increases with, when the duration increases with 1 day (and all other variables are held equal). As this
was modelled with a linear regression, an assumption is that the effect of durset on eprice is linear.
This could be violated if the relationship is not linear. For example, it could be the case that
eprice indeed increases as durset increases, but that this effect slows down at around 5 days, and
then starts to approach some limit. This could happen if a longer duration initially allows more potential
buyers to see the product and thus allows for a greater number of bids. However, after some days
most potential bidders have seen the product, and longer durations do not increase the price by a
meaningful amount anymore. This would be a logarithmic relationship
3b)
While both the median spline and the fitted values follow a similar trajectory across all values
of durset, the median spline does slightly deviate from the linear fit.
The median spline is not perfectly straight, but shows a subtle deviation that suggests there
could be some curvature in the relationship between durset and eprice. The median spline starts with
a slight upward bend and is followed by a potential flattening and/or dip at the higher values of durset,
possibly suggesting an inversely U-shaped curvature.
4a)
Adding a second-degree polynomial term (durset2) to the semilog model allows us to capture a
more complex relationship between auction duration (durset) and the final price (eprice). This
approach goes beyond the assumption of linearity and tests for an inverted u-shaped relationship,
where there is an optimal auction duration that maximizes the final price.
From the model, the coefficient of durset is 0.50, indicating that initially, each additional auction
day increases the price. However, the coefficient of durset 2 is -0.05, which is negative and significant.
This suggests that after a certain point, the effect of longer auction durations becomes negative,
leading to a decline in the final price.
These coefficients together confirm an inverted u-shape: prices rise with increasing auction
duration, reach a peak, and then begin to fall. This aligns with expectations—short auctions may not
attract enough bidders, while overly long auctions may cause buyers to lose interest or reduce
competition.
The presence of a significant negative durset2 term helps pinpoint the optimal auction duration.
At this duration, sellers achieve the highest price on average.
4b)
To determine the value of durset at which sellers achieve the maximum price (eprice), we
need to find the peak of the polynomial function y = a + bx + cx 2. This involves calculating the point
where the first derivative equals zero, as this indicates the maximum of the curve.
To Find the Maximum:
The polynomial function is:
y=a+b⋅x+c⋅x2
To find the peak, take the derivative and set it equal to zero:
dydx=b+2c⋅x
1
