Question by : Multiple Regression Question?
please help:
For a multiple regression with three explanatory variables the value of R2 is 0.75.
Indicate whether each of the following statements is true or false and give brief reasons for your answer:
(i)The three explanatory variables each explain 25% of the variation in the dependent variable.
(ii)If R2 = 0.75 then three quarters of the data is perfectly explained by the model.
(iii)The most important factor when comparing this model with any others is to find the highest R2.
(iv)The higher the value of R2, the greater the probability the model is correct.
Explain the difference between the usual (product moment) correlation and rank correlation. In what situations is it more appropriate to use rank correlation?
(30 marks)
Best answer:
Answer by cidyah
i) The three explanatory variables each explain 25% of the variation in the dependent variable.
Not true. The three variables as a whole account for 75% of the variation in the dependent variable.
(ii) If R2 = 0.75 then three quarters of the data is perfectly explained by the model.
Not true. 75% of the variation in the entire data is explained by the model.
(iii) The most important factor when comparing this model with any others is to find the highest R2.
True. We want the R^2 to be as large as possible so we can expain the variation in the dependent variable at best by using the three independent variable.
(iv) The higher the value of R2, the greater the probability the model is correct.
you may want to go through the link.
Product moment correlation measures the strength of linear association between two variables. Rank correlation is nonparametric that it can be used for ordinal data whereas Pearson correlation requires that they be interval or ratio scaled data. When we compare the degree of similarity of two rankings, (two judges judging the contestants of a contest), rank correlation is more appropriate. Product moment correlation requires bivariate normality assumption whereas the rank correlation doesn’t.
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