Question

Ornithologists, scientists who study birds, tag sparrow hawks in 13 different colonies to study their population. They gather data for the percent of new sparrow hawks in each colony and the percent of those that have returned from migration.
Percent return:74; 66; 81; 52; 73; 62; 52; 45; 62; 46; 60; 46; 38
Percent news; 6; 8; 11; 12; 15; 16; 17; 18; 18; 19; 20; 20

a. Enter the data into your calculator and make a scatter plot.
b. Use your calculator's regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a.
c. Explain in words what the slope and y-intercept of the regression line tell us.
d. How well does the regression line fit the data? Explain your response.
e. Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
f. An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 70% of the adults from the previous year have returned. What is the prediction?

Answer 1

Answer:

Step-by-step explanation:

Hello!

The variables of interest are:

Y: % of new sparrow hacks.

X: % of sparrow hacks that return after migration.

a. see attachment

b. Using a statistics software I've estimated the regression line:

^Y= 30.29 -0.26X

The second attachment shows scatterplot with the estimated regression line.

c.

The estimated slope is 30.29

30.29% is the estimated average percentage of new sparrows hawk in the colony when the percentage of returned sparrow hawks is zero.

-0.29 is the modification of the estimated average percentage of new sparrow hawks in the colony when the percentage of returned sparrow hawks increases by 1%.

d. To know how does the model fits the regression you have to calculate the determination coefficient.

R²= 0.43

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Its range is from 0 to 1, where zero means that the regression line doesn't fit the data and 1 means that there is a perfect fit.

Now for the estimated model, only 43% of its variability is given by the explanatory variable, this is too low so the data doesn't fit the model.

e. The residues represent the distance between each observation Yi and the regression line, symbolically:

ei= Yi-^Yi

The % of new sparrow hawks that is further away from the regression line is Y=8, the residue corresponding to this value is ei= -5.45

f. You need to predict the percentage of new birds in the colony if the return percentage is 70%, symbolically:

Y/X=70

To do so you need to replace the given value of X is the estimated regression model:

^Y= 30.29 -0.26X

^Y= 30.29 -0.26*10

^Y= 12.09%

I hope this helps!