A) If a regression experiment has correlation coefficient r= 0.75, what precent of total variation is explained by the regression?
B) if 85% of total variation is explained by the regression, and there is an inverse relationship between y and x, then what is the correlation coefficient?
C) if 30% of the total variation is not explained by the regression, then what is the correlation coefficient? Assume a direct relationship between y and x.
The coefficient of determination deals with variation and is a measure of how well any given regression line represents its data. If a regression line passes through every point, all of the variation could be explained. The further the regression line is away from the points, the less can be explained.
You square the correlation coefficient to get the coefficient of determination.
Let's look at Part A as an example. If r = 0.75, then r^2 = 0.5625, which means that approximately 56% of the total variation in y can be explained by the linear relationship between x and y. The other 44% of the total variation in y is unexplained.
I hope this will help get you started.
burat
A) Ah, correlation coefficients, the masters of explaining relationships. So, if we have a correlation coefficient of 0.75, it means that 75% of the total variation is explained by the regression.
B) Inverse relationship, huh? Sounds like a complicated love story. If 85% of the total variation is explained by the regression, then the correlation coefficient would be the square root of 1 minus 0.85. Just don't ask me to do the actual math, I'm more about the jokes than numbers.
C) Ah, the rebels! If 30% of the total variation is not explained by the regression, it means that the remaining 70% is. So, the correlation coefficient would be the square root of 0.70, assuming a direct relationship between y and x. I don't know about you, but I'd love to know what happened to that 30% of rebellious variation. Must be an interesting story!
A) To find the percent of total variation explained by the regression when the correlation coefficient is given, you can square the correlation coefficient (r) and multiply it by 100%.
In this case, if r = 0.75, then to find the percent of total variation explained by the regression:
(0.75)^2 * 100% = 0.5625 * 100% = 56.25%
Therefore, 56.25% of the total variation is explained by the regression.
B) If 85% of the total variation is explained by the regression and there is an inverse relationship between y and x, you need to find the square root of the complement of the explained variation to calculate the correlation coefficient.
The complement of the explained variation is 100% - 85% = 15%. Taking the square root of the complement of the explained variation gives you the absolute value of the correlation coefficient.
So, the correlation coefficient in this scenario is √15% = √0.15 ≈ 0.387.
However, since there is an inverse relationship between y and x, the correlation coefficient will be negative. So, the final correlation coefficient is approximately -0.387.
C) If 30% of the total variation is not explained by the regression and there is a direct relationship between y and x, you need to find the square root of the complement of the unexplained variation to calculate the correlation coefficient.
The complement of the unexplained variation is 30%, which means that 70% is explained by the regression. Taking the square root of the complement of the unexplained variation gives you the absolute value of the correlation coefficient.
So, the correlation coefficient in this scenario is √70% = √0.7 ≈ 0.837.
Since there is a direct relationship between y and x, the final correlation coefficient is positive, approximately 0.837.