The Conde Nast Traveler Gold List for 2012 provided rating for the top 20 small cruise ships. The data from annual Readers’ Choice Survey are the overall scores(Y) each ship received based on several criteria, including Itineraries/Schedule (X1), Shore Excursions(X2), and Food/Dinning(X3). The estimated regression equation to predict the overall scores is Y= 35.6184+0.1105 X1+0.2445 X2+0.2474 X3. Part of the regression results is shown below. Coefficients Standard Error Intercept 35.6184 13.2308 Itineraries/Schedule(X1) 0.1105 0.1297 Shore Excursions(X2) 0.2445 0.0434 Food/Dinning(X3) 0.2474 0.0621 Use the T test to determine whether or not the coefficient of X1 is significant. Use Level of significance=.05? Be sure to state null and alternative hypotheses. Use the t test to determine whether or not the coefficient of X2 is significant. Use the level if significance=.05? Be sure to sate the null and alternative hypotheses. Use the T test to determine whether or not the coefficient of X3 is significant. Use level of significance =.05? Be sure to state the null and the alternative hypotheses. Do you think that any independent variable should be dropped from the model? Explain based on your answers for parts (a)-(c).
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 Conde Nast Traveler Gold List for 2012 provided rating for the top 20 small cruise ships. The data from annual Readers’ Choice Survey are the overall scores(Y) each ship received based on several criteria, including Itineraries/Schedule (X1), Shore Excursions(X2), and Food/Dinning(X3). The estimated regression equation to predict the overall scores is
Y= 35.6184+0.1105 X1+0.2445 X2+0.2474 X3. Part of the regression results is shown below.
Coefficients Standard Error
Intercept 35.6184 13.2308
Itineraries/Schedule(X1) 0.1105 0.1297
Shore Excursions(X2) 0.2445 0.0434
Food/Dinning(X3) 0.2474 0.0621
- Use the T test to determine whether or not the coefficient of X1 is significant. Use Level of significance=.05? Be sure to state null and alternative hypotheses.
- Use the t test to determine whether or not the coefficient of X2 is significant. Use the level if significance=.05? Be sure to sate the null and alternative hypotheses.
- Use the T test to determine whether or not the coefficient of X3 is significant. Use level of significance =.05? Be sure to state the null and the alternative hypotheses.
- Do you think that any independent variable should be dropped from the model? Explain based on your answers for parts (a)-(c).
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