3.Binary Categorical Variables: Weight Based on Height and Gender Categorical variables with only two categories (such as male/female or yes/no) can be used in a multiple regression model if we code the answers with numbers. We have looked at a simple linear model to predict Weight based on Height. What role does gender play? If a male and a female are the same height, do we predict the same weight for both of them? Is gender a significant factor in predicting weight? We can answer these questions by using a multiple regression model to predict weight based on height and gender. Using 1 for females and 0 for males in a new variable called GenderCode in the dataset StudentSurvey, we obtain the following output. The regression equation is Weight = -23.9 + 2.86Height - 25.5GenderCode Predictor Coef SE Coef T P Constant -23.92 27.36 -0.87 0.383 Height 2.8589 0.3855 7.42 0.000 GenderCode -25.470 3.138 -8.12 0.000 S = 22.8603 R - Sq = 48.2% R - Sq (adj) = 47.9% (a) What weight does the model predict for a male who is 5'5'' ( 65 inches)? For a female who is 5'5''? Round your answers to two decimal places. b) Which of the variables which are significant at the 5% level?
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.
3.Binary Categorical Variables: Weight Based on Height and Gender
Categorical variables with only two categories (such as male/female or yes/no) can be used in a multiple regression model if we code the answers with numbers. We have looked at a simple linear model to predict Weight based on Height. What role does gender play? If a male and a female are the same height, do we predict the same weight for both of them? Is gender a significant factor in predicting weight? We can answer these questions by using a multiple regression model to predict weight based on height and gender. Using 1 for females and 0 for males in a new variable called GenderCode in the dataset StudentSurvey, we obtain the following output.
The regression equation is Weight = -23.9 + 2.86Height - 25.5GenderCode
| Predictor | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | -23.92 | 27.36 | -0.87 | 0.383 |
| Height | 2.8589 | 0.3855 | 7.42 | 0.000 |
| GenderCode | -25.470 | 3.138 | -8.12 |
0.000 |
S = 22.8603 R - Sq = 48.2% R - Sq (adj) = 47.9%
(a) What weight does the model predict for a male who is 5'5'' ( 65 inches)? For a female who is 5'5''? Round your answers to two decimal places.
b) Which of the variables which are significant at the 5% level?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
