The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($000) 1 9 8.1 2 7 6.0 3 11 3.6 4 12 4.0 5 8 5.0 6 7 10.0 7 8 7.6 8 11 8.0 9 10 8.0 10 12 6.0 11 6 8.6 12 6 8.0 Click here for the Excel Data File If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) x y x−x¯x-x¯ y−y¯y-y¯ (x−x¯)2x-x¯2 (y−y¯)2y-y¯2 (x−x¯) (y−y¯)x-x¯ y-y¯ 9.0 8.1 1.192 0.007 1.420 0.099 7.0 6.0 −0.908 3.674 0.825 1.741 11.0 3.6 2.083 4.340 10.945 −6.892 12.0 4.0 3.083 9.507 8.458 −8.967 8.0 5.0 −0.917 −1.908 3.642 1.749 7.0 10.0 −1.917 3.092 9.558 −5.926 8.0 7.6 −0.917 0.692 0.840 −0.634 11.0 8.0 2.083 1.092 4.340 2.274 10.0 8.0 1.083 1.092 1.174 1.192 12.0 6.0 3.083 −0.908 9.507 0.825 6.0 8.6 −2.917 1.692 8.507 2.862 −4.934 6.0 8.0 −2.917 1.092 8.507 1.192 −3.184 107.0 82.9 x¯x¯ = y¯y¯ = Sx = Sy = r = b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.) Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to the nearest whole number.)
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 owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
| Car | Age (years) | Selling Price ($000) | ||||||||
| 1 | 9 | 8.1 | ||||||||
| 2 | 7 | 6.0 | ||||||||
| 3 | 11 | 3.6 | ||||||||
| 4 | 12 | 4.0 | ||||||||
| 5 | 8 | 5.0 | ||||||||
| 6 | 7 | 10.0 | ||||||||
| 7 | 8 | 7.6 | ||||||||
| 8 | 11 | 8.0 | ||||||||
| 9 | 10 | 8.0 | ||||||||
| 10 | 12 | 6.0 | ||||||||
| 11 | 6 | 8.6 | ||||||||
| 12 | 6 | 8.0 | ||||||||
Click here for the Excel Data File
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If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable?
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b-1. Determine the
correlation coefficient . (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
| x | y | x−x¯x-x¯ | y−y¯y-y¯ | (x−x¯)2x-x¯2 | (y−y¯)2y-y¯2 | (x−x¯) (y−y¯)x-x¯ y-y¯ | |||||||||||||||
| 9.0 | 8.1 | 1.192 | 0.007 | 1.420 | 0.099 | ||||||||||||||||
| 7.0 | 6.0 | −0.908 | 3.674 | 0.825 | 1.741 | ||||||||||||||||
| 11.0 | 3.6 | 2.083 | 4.340 | 10.945 | −6.892 | ||||||||||||||||
| 12.0 | 4.0 | 3.083 | 9.507 | 8.458 | −8.967 | ||||||||||||||||
| 8.0 | 5.0 | −0.917 | −1.908 | 3.642 | 1.749 | ||||||||||||||||
| 7.0 | 10.0 | −1.917 | 3.092 | 9.558 | −5.926 | ||||||||||||||||
| 8.0 | 7.6 | −0.917 | 0.692 | 0.840 | −0.634 | ||||||||||||||||
| 11.0 | 8.0 | 2.083 | 1.092 | 4.340 | 2.274 | ||||||||||||||||
| 10.0 | 8.0 | 1.083 | 1.092 | 1.174 | 1.192 | ||||||||||||||||
| 12.0 | 6.0 | 3.083 | −0.908 | 9.507 | 0.825 | ||||||||||||||||
| 6.0 | 8.6 | −2.917 | 1.692 | 8.507 | 2.862 | −4.934 | |||||||||||||||
| 6.0 | 8.0 | −2.917 | 1.092 | 8.507 | 1.192 | −3.184 | |||||||||||||||
| 107.0 | 82.9 | ||||||||||||||||||||
| x¯x¯ | = | y¯y¯ | = | Sx | = | Sy | = |
| r | = |
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b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.)
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Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to the nearest whole number.)
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