Tar 25 27 20 24 20 20 21 24 CO 18 16 16 16 16 16 14 17 Nicotine 1.5 1.7 1.1 1.6 1.1 1.0 1.2 1.4 Multiple Regression with Cigarettes Use the sample data given in Exercise 1 “Cigarette Tar and Nicotine.” a. Find the multiple regression equation with the response (y) variable of amount of nicotine and predictor (x) variables of amounts of tar and carbon monoxide. b. Identify the value of the multiple coefficient of determination R2, the adjusted R2, and the P-value representing the overall significance of the multiple regression equation.c. Use a 0.05 significance level and determine whether the regression equation can be used to predict the amount of nicotine given the amounts of tar and carbon monoxide. d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar and 15 mg of carbon monoxide. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine?
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.
|
Tar |
25 |
27 |
20 |
24 |
20 |
20 |
21 |
24 |
|
CO |
18 |
16 |
16 |
16 |
16 |
16 |
14 |
17 |
|
Nicotine |
1.5 |
1.7 |
1.1 |
1.6 |
1.1 |
1.0 |
1.2 |
1.4 |
Multiple Regression with Cigarettes Use the sample data given in Exercise 1 “Cigarette Tar and Nicotine.”
a. Find the multiple regression equation with the response (y) variable of amount of nicotine and predictor (x) variables of amounts of tar and carbon monoxide.
b. Identify the value of the multiple coefficient of determination R2, the adjusted R2, and the
P-value representing the overall significance of the multiple regression equation.
c. Use a 0.05 significance level and determine whether the regression equation can be used to
predict the amount of nicotine given the amounts of tar and carbon monoxide.
d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar and 15 mg of carbon monoxide. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine?
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