Let x be per capita income in thousands of dollars. let y be the number of medical doctors per 10,000 residents. six small cities in oregon gave the following information about x and y.

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.

answer; interviews;