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lubasha [3.4K]
3 years ago
10

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

with variables x and y . What is closest to the proportion of the variation in y that cannot be explained by the explanatory variable?
Mathematics
1 answer:
Makovka662 [10]3 years ago
8 0

Answer:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

And the model obtained for this case is:

y = -3.4 +5.2 x

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

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