Question

State casket sales restrictions. Some states permit only licensed firms to sell funeral goods (e.g., caskets, urns) to the consumer, while other states have no restrictions. States with casket sales restrictions are being challenged in court to lift these monopolistic restrictions. A paper in the Journal of Law and Economics (February 2008) used multiple regression to investigate the impact of lifting casket sales restrictions on the cost of a funeral. Data collected for a sample of 1,437 funerals were used to fit the model. A simpler version of the model estimated by the researchers is, $E\left(y\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_1{x}_2$where y is the price (in dollars) of a direct burial, x₁ = {1 if funeral home is in a restricted state, 0 if not}, and x₂ = {1 if price includes a basic wooden casket, 0 if no casket}. The estimated equation (with standard errors in parentheses) is:$y^=1432+793x_1-252x_2+261x_1{x}_{2,}$

, R² = 0.78

(70) (134) (109)

1. Calculate the predicted price of a direct burial with a basic wooden casket at a funeral home in a restricted state.
2. The data include a direct burial funeral with a basic wooden casket at a funeral home in a restricted state that costs \(2,200. Assuming the standard deviation of the model is \)50, is this data value an outlier?
3. The data also include a direct burial funeral with a basic wooden casket at a funeral home in a restricted state that costs \(2,500. Again, assume that the standard deviation of the model is \)50. Is this data value an outlier?

Short answer

1. The predicted price of a direct burial with a basic wooden casket at a funeral home in a restricted state is $2234.
2. The value $2,200 lies within the +/- 3-sigma limit hence this data value is not an outlier.
3. The value $2,500 lies outside the +/- 3-sigma limit hence this data value is an outlier.

Step-by-step solution

Predicted price

The predicted price of a direct burial with a basic wooden casket at a funeral home in a restricted state can be estimated when the value of x₁ = 1 and x₂ = 1;

$$\begin{gathered} \hat{y}=1432+793x_1-252x_2+261x_1{x}_2 \\ \hat{y}=1432+793\left(1\right)-252\left(1\right)+261\left(1\right)\left(1\right) \\ \hat{y}=2234 \end{gathered}$$

Therefore, the predicted price of a direct burial with a basic wooden casket at a funeral home in a restricted state is $2234.

Outlier

The value of an outlier is determined by +/- 3σ from the mean. The mean value here is $2,234 with standard deviation being $50. The 3-sigma limit becomes $2,384.

The value $2,200 lies within the +/- 3-sigma limit hence this data value is not an outlier.

Outlier

The value of an outlier is determined by +/- 3σ from the mean. The mean value here is $2,234 with standard deviation being $50. The 3-sigma limit becomes $2,384.

The value $2,500 lies outside the +/- 3-sigma limit hence this data value is an outlier.