Researchers monitoring the number of wolves and rabbits in a wildlife reserve think that the size of the wolf popu lation depends on the rabbit population, since wolves eat rabbits. Over the years, the researchers have collected the following data.

Rabbit population 61 72 78 76 65 54 39 43
Wolf population 26 33 42 49 37 30 24 19
a) Generate a scatter plot for the data with the independent variable on the x-axis.
b) Given that the equation of the regression line is y = 0.58x – 3.10, how many wolves would the regression equation predict when the number of rabbits is zero?
c) Given that R2 = 0.7486, calculate the correlation coefficient. Does it indicate a weak or a strong relationship?
d) Calculate the residual values of all data points.

a) Since the number of wolves depend on the number of rabbits, it means that the rabbit population is the independent variable. Hence, plot each of the given points on your graph with the x-axis labelled as the number of rabbits and the y-axis as the number of wolves.

b) In your regression equation, put the value of x as 0 and solve for y.

c) Ok, for this one, I had to look it up.

If -1 \leq r \leq 0 there is a negative linear correlation, where r = -1 indicating perfect negative linear correlation.

If 0\leq r \leq 1 there is a positive linear correlation, where r = 1 indicating perfect positive linear correlation.

If r =0 there is a no correlation.

Can you do it now?

d) I had to look that up too...

The residual value of each point is given by the amount by which the point is 'far from' the regression line, in the direction of the y-axis.

e = y - \hat{y}

Where y is the actual value and \hat{y} the predicted value.

I still don't know how to make the graph can u please show me

Here's a scatter plot. It's not too great, but I can't find any better...

http://p1cture.me/images/50473897966513921178.png

Can u just show me how to do part d thankss

If I understood well, the equation of the line is y = 0.58x + 3.10

For the first point, we have (61, 26)

The value given by the regression line is however y = 0.58(61) + 3.10 = 38.48

which is (61, 38.48)

Hence, the residual value for this point is 26 - 38.48 = -12.48

If I understood well, the equation of the line is y = 0.58x + 3.10
is this is how it should be for the second point

For the second point, we have (72, 33)
The value given by the regression line is however y = 0.58(72) + 3.10 = 44.86
which is (72, 44.86)
Hence, the residual value for this point is 33 - 44.86 = -11.86

this is the calculation we have to do for all of the points

Yes, that's it and yes, you'll have to do this for every point.