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Answer:
The percentage of variation esplained by the model is given by the determination coefficient, on this case:
And we have 87.2% of the variation explained by the linear model given.
And we have 12.031 doctors per 10000 residents.
Explanation:
Assuming the following dataset:
x y
8.6 9.6
9.3 18.5
10.1 20.9
8.0 10.2
8.3 11.4
8.7 13.1
Assuming this question: "The data has a correlation coefficient of r = 0.934. Calculate the regression line for this data. What percentage ofvariation is explained by the regression line? Predict the number of doctors per 10,000 residents in a town with a per capita income of $8500."
We want a linear model like this:
Where m represent the slope and b the intercept for the linear model. And we cna find the slope and b with the following formulas:
And from the dataset we have the following values:
And replacing into the equation for m we got:
And the intercept:
And then the linear model is given by:
We can find the estimation replacing x = 8.5 into the linear model and we got:
And we have 12.031 doctors per 10000 residents.
The percentage of variation esplained by the model is given by the determination coefficient, on this case:
And we have 87.2% of the variation explained by the linear model given.