Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept) Height Cabinets Estimate -57.9877 1.276 0.3393 Std. Error 8.6382 0.2643 0.1302 t value -6.713 4.828 2.607 Pr(>|t|) 2.75e-07 4.44e-05 0.0145 Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example? The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches. The constant term always has a meaningful interpretation. In this example the area of the kitchen is predicted to be 57.99% smaller if additional cabinets were added. The predicted height will be negative when the number of cabinets is zero and the area of the kitchen is zero. But we cannot have a negative area!
Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers:
Area – area of the kitchen in square feet
Height – ceiling height in the kitchen (from floor to ceiling) in inches
Cabinets – number of cabinets in the kitchen
Suppose that a multiple linear regression model was fit to the data and that the following output resulted:
| Coefficients: | ||||
(Intercept) Height Cabinets |
Estimate -57.9877 1.276 0.3393 |
Std. Error 8.6382 0.2643 0.1302 |
t value -6.713 4.828 2.607 |
Pr(>|t|) 2.75e-07 4.44e-05 0.0145 |
Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example?
The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches.
The constant term always has a meaningful interpretation. In this example the area of the kitchen is predicted to be 57.99% smaller if additional cabinets were added.
The predicted height will be negative when the number of cabinets is zero and the area of the kitchen is zero. But we cannot have a negative area!
.jpg)
Step by step
Solved in 2 steps with 2 images
