Final answer:
Multiple regression is used to predict outcomes given a set of predictor variables. In the hardwood installation example, the accuracy and relevance of predictions depend on the variables used in the model. These methods can similarly apply to different fields, such as crime modeling, where regression models help in decision making.
Step-by-step explanation:
The question pertains to multiple regression, which is a statistical technique used to model the relationship between a dependent variable and multiple independent variables. When a contractor specializing in hardwood floors uses a regression model to predict the cost of installing a new floor, the approach taken can vary:
- Utilizing only one predictor variable may give a rough estimate, but could overlook important factors influencing cost.
- Including both hardwood and labor costs as predictor variables can provide a more accurate prediction.
- Ignoring the regression model entirely will not leverage the benefits of statistical analysis, possibly leading to inaccurate estimates.
- Using a random number generator for predictions would not be advisable as it does not consider any real-world data and can lead to nonsensical estimates.
In the context of modeling crime, one must first map correlated data before applying regression models. Law enforcement officials can then use these models to deploy resources more effectively. For example, city officials estimating the impact of a new liquor store on crime rates would utilize a regression model to analyze the effect of the store on local crime, considering variables such as income, education, and presence of similar establishments.
When predicting sales growth using a regression model given by ŷ = 101.32 + 2.48x, we can make predictions for specific days. On day 60, the predicted sales would be ŷ = 101.32 + (2.48 × 60). On day 90, the sales prediction adjusts accordingly based on the day.