The following are the age (in years) and price (in hundreds of dollars) data for a certain type of car. A scatterplot of the data is given to the right. 500- 400- 300 Age (x) 6 Price (y) 273 265 279 401 363 295 330 315 406 307 6 3 1 1 6 8 10 a. Obtain the linear correlation coefficient. b. Interpret the value of r in terms of the linear relationship between the two variables. c. Discuss the graphical interpretation of the value of r. d. Obtain the value of the coefficient of determination by squaring r. a.r= (Round to.three decimal places as needed.) b. There is V between the two variables v as the x-values increase, and the data points appear c. The given graph is V with the interpretation found in part (b), because the y-values appear to d. = (Round to three decimal places as needed.)
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.
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Correlation Coefficient:
It is one of the statistical measures. It is used between any two variables in order to know the strength of the linear relationship of those two variables. The value of the correlation coefficient lies between -1 to 1(including zero).
If the correlation coefficient positive then it is positively linearly correlated, if it is negative then it is negatively linearly correlated, and if it is zero then there is no linear correlation between the variables. When the correlation coefficient reaching the maximum or the minimum value (i.e., -1 or1) then the variables are very strongly related to each other.
r=, Cov(x,y) is the covariance of x and y; σx is the standard deviation of x; σy is the standard deviation of y.
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