Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue to increase in value. The data showing the rarity rating (1–20) and the high price ($1000s) for 15 classic cars is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions. Open spreadsheet Develop a scatter diagram of the data using the rarity rating as the independent variable and price as the dependent variable. Does a simple linear regression model appear to be appropriate? A simple linear regression model _________appearsdoes not appear to be appropriate. Develop an estimated multiple regression equation with rarity rating and as the two independent variables. (to whole numbers) What is the value of the coefficient of determination? Note: report between 0 and 1. (to 3 decimals) What is the value of the test statistic? (to 2 decimals) What is the -value? (to 4 decimals) Consider the nonlinear relationship shown by equation . Use logarithms to develop an estimated regression equation for this model. (to 3 decimals) What is the value of the coefficient of determination? Note: report between 0 and 1. (to 3 decimals) What is the value of the test statistic? (to 2 decimals) What is the -value? (to 4 decimals) Do you prefer the estimated regression equation developed in part (b) or part (c)? Explain. The model in part _____(b)(c) is preferred because it provides a better fit.
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.
Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue to increase in value. The data showing the rarity rating (1–20) and the high price ($1000s) for 15 classic cars is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.
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Develop a
scatter diagram of the data using the rarity rating as the independent variable and price as the dependent variable. Does a simple linear regression model appear to be appropriate?A simple linear regression model _________appearsdoes not appear to be appropriate.
-
Develop an estimated multiple regression equation with rarity rating and as the two independent variables.
(to whole numbers)What is the value of the coefficient of determination? Note: report between 0 and 1.
(to 3 decimals)
What is the value of the test statistic?
(to 2 decimals)
What is the -value?
(to 4 decimals)
-
Consider the nonlinear relationship shown by equation . Use logarithms to develop an estimated regression equation for this model.
(to 3 decimals)What is the value of the coefficient of determination? Note: report between 0 and 1.
(to 3 decimals)
What is the value of the test statistic?
(to 2 decimals)
What is the -value?
(to 4 decimals)
-
Do you prefer the estimated regression equation developed in part (b) or part (c)? Explain.
The model in part _____(b)(c) is preferred because it provides a better fit.
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