91影视

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 new:\(5; 6; 8; 11; 12; 15; 16; 17; 18; 18; 19; 20; 20\)

a. Enter the data into your calculator and make a scatter plot.

b. Use your calculator鈥檚 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.

The following table shows data on average per capita coffee consumption and heart disease rate in a random sample of \(10\) countries.

a. Enter the data into your calculator and make a scatter plot.

b. Use your calculator鈥檚 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.

75. The following table consists of one student athlete's time (in minutes) to swim 2000 yards and the student's heart rate (beats per minute) after swimming on a random sample of 10 days:

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.

A researcher is investigating whether population impacts homicide rate. He uses demographic data from Detroit, MI to compare homicide rates and the number of the population that are white males.

a. Use your calculator to construct a scatter plot of the data. What should the independent variable be? Why?

b. Use your calculator鈥檚 regression function to find the equation of the least-squares regression line. Add this to your

scatter plot.

c. Discuss what the following mean in context.

i. The slope of the regression equation

ii. The y-intercept of the regression equation

iii. The correlation \(r\)

iv. The coefficient of determination \(r2\).

Using the data to determine the linear-regression line equation with the outliers removed. Is there a linear correlation for the data set with outliers removed? Justify your answer.

The average number of people in a family that attended college for various years is given in Table 12.29.

a. Using 鈥測ear鈥� as the independent variable and 鈥淣umber of Family Members Attending College鈥� as the dependent variable, draw a scatter plot of the data.

b. Calculate the least-squares line. Put the equation in the form of: \(\hat{y}=a+bx\)

c. Find the correlation coefficient. Is it significant?