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Can A regression equation have a negative coefficient of correlation and a negative coefficient of determination?
Wiki User
∙ 9y ago
It's not quite possible for the coefficient of determination to be negative at all, because of its definition as r2 (coefficient of correlation squared). The coefficient of determination is useful since tells us how accurate the regression line's predictions will be but it cannot tell us which direction the line is going since it will always be a positive quantity even if the correlation is negative. On the other hand, r (the coefficient of correlation) gives the strength and direction of the correlation but says nothing about the regression line equation. Both r and r2 are found similarly but they are typically used to tell us different things.
Wiki User
∙ 9y ago
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Do you need more than 10 observations in linear regression?
This is a difficult question to answer. The pure answer is no. In reality, it depends on the level of randomness in the data. If you plot the data, it will give you an idea of the randomness. Even with 10 data points, 1 or 2 outliers can significantly change the regression equation. I am not aware of a rule of thumb on the minimum number of data points. Obviously, the more the better. Also, calculate the correlation coefficient. Be sure to follow the rules of regression. See the following website: http:/www.duke.edu/~rnau/testing.htm
How do you calculate regression equation?
what is the equation of the regression line for the given data(Age, Number of Accidents) (16, 6605), (17, 8932), (18, 8506), (19, 7349), (20, 6458), (21, 5974)
The random error in a regression equation?
includes both positive and negative terms.
The regression equation is determined by minimizing?
The total squared error between the predicted y values and the actual y values
How do you interpret coefficient of dummy variable?
To interpret the coefficient of a dummy variable is to follow all of the steps of the equation that is being used as if the dummy variable was a real one.
What is regression coefficient and correlation coefficient?
The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.
Explain the concept of correlation and regression line as a forecasting tool?
once an equation for a regression is derived it can be used to predict possible future
When a pair of variables have a positive correlation will the slope in the regression equation always be positive?
Yes
How do you calculate coefficient of determination by using TI 84 Plus calculator?
Enter the data into 2 lists such as L1 and L2. You do this by going to [STAT] and hit [ENTER] on [EDIT]. After you do this then go turn on diagnostic by going to [2ND] [0] scrolling down to Diagnostic on. Then go back to [STAT], right the right arrow to CALC and scroll down the appropriate regression. Once you have chosen the right regression go to [2ND] [1][,][2ND][2][ENTER] this will give you the equation and coefficient of determination
How do you calculate coefficient of determination by using TI-84 Plus calculator?
Enter the data into 2 lists such as L1 and L2. You do this by going to [STAT] and hit [ENTER] on [EDIT]. After you do this then go turn on diagnostic by going to [2ND] [0] scrolling down to Diagnostic on. Then go back to [STAT], right the right arrow to CALC and scroll down the appropriate regression. Once you have chosen the right regression go to [2ND] [1][,][2ND][2][ENTER] this will give you the equation and coefficient of determination
How does the time period or number of variables effect correlation coefficient?
The time period may not affect the correlation coefficient at all. If looking at the correlation between the mass and volume of steel objects, time is totally irrelevant. The effect of the number of variables depends on whether or not the extra variables are related to ANY of the variables in the equation.
What is the adjective of the word regression?
of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
What is the difference between correlation analysis and regression analysis?
In linear correlation analysis, we identify the strength and direction of a linear relation between two random variables. Correlation does not imply causation. Regression analysis takes the analysis one step further, to fit an equation to the data. One or more variables are considered independent variables (x1, x2, ... xn). responsible for the dependent or "response" variable or y variable.
What is the difference between corelation and regression?
I've included links to both these terms. Definitions from these links are given below. Correlation and regression are frequently misunderstood terms. Correlation suggests or indicates that a linear relationship may exist between two random variables, but does not indicate whether X causes Yor Y causes X. In regression, we make the assumption that X as the independent variable can be related to Y, the dependent variable and that an equation of this relationship is useful. Definitions from Wikipedia: In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. In statistics, regression analysis refers to techniques for the modeling and analysis of numerical data consisting of values of a dependent variable (also called a response variable) and of one or more independent variables (also known as explanatory variables or predictors). The dependent variable in the regression equation is modeled as a function of the independent variables, corresponding parameters ("constants"), and an error term. The error term is treated as a random variable. It represents unexplained variation in the dependent variable. The parameters are estimated so as to give a "best fit" of the data. Most commonly the best fit is evaluated by using the least squares method, but other criteria have also been used.
Do you need more than 10 observations in linear regression?
This is a difficult question to answer. The pure answer is no. In reality, it depends on the level of randomness in the data. If you plot the data, it will give you an idea of the randomness. Even with 10 data points, 1 or 2 outliers can significantly change the regression equation. I am not aware of a rule of thumb on the minimum number of data points. Obviously, the more the better. Also, calculate the correlation coefficient. Be sure to follow the rules of regression. See the following website: http:/www.duke.edu/~rnau/testing.htm
What is the only condition under which (x y) regression equation solved for x gives the same predictions as the (y x) regression equation?
If the regression is a perfect fit.
What can you conclude if the global test of regression does not reject the null hypothesis?
You can conclude that there is not enough evidence to reject the null hypothesis. Or that your model was incorrectly specified. Consider the exact equation y = x2. A regression of y against x (for -a < x < a) will give a regression coefficient of 0. Not because there is no relationship between y and x but because the relationship is not linear: the model is wrong! Do a regression of y against x2 and you will get a perfect regression!
