The following regression equation gives the relationship between the number of Fake Christmas trees sold each year in a certain state and the number of Real Christmas trees sold that same year in that state: Fake = 8162 - 0.11(Real)(a) How many fake Christmas trees would you predict for a year in which 9211 real Christmas trees sold? (2 decimal places) (b) This model has an R-squared value of 0.1. What is the correlation between the number of real and fake trees sold? (3 decimal places) (c) A competing model predicting the number of fake trees sold using the number families with children under age 8 has an R-squared value of 0.21. Which model should we prefer? We should prefer the model using the number of real trees sold.We should prefer the model using the number of children under age 8. We should not have a preference between the two models.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The following regression equation gives the relationship between the number of Fake Christmas trees sold each year in a certain state and the number of Real Christmas trees sold that same year in that state:
(a) How many fake Christmas trees would you predict for a year in which 9211 real Christmas trees sold? (2 decimal places)
(b) This model has an R-squared value of 0.1. What is the
(c) A competing model predicting the number of fake trees sold using the number families with children under age 8 has an R-squared value of 0.21. Which model should we prefer?
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