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Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years and what influences it is a concern in U.S. colleges and universities.

US News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the per centage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

a. Draw a scatterplot of the data.

b. Is finding a regression line for the data reasonable? Explain your answer.

c. Determine the regression equation for the data, and draw its graph

on the scatterplot you drew in part (a).

d. Describe the apparent relationship between student-to-faculty

ratio and graduation rate.

e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?

f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.

g. Identify outliers and potential influential observations

Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24hr$birth weights are in hectograms.

a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) (d).

b. Obtain the coefficient of determination.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression. and interpret your answer.

d. State how useful the regression equation appears to be for making predictions.

The symbol that is used for the linear correlation coefficient is -------

The coefficient of determination of a set of data points is $0.70y$and the slope of the regression line is $-3.58$. Determine the linear correlation coefficient of the data.

Fill in the blank.

The graph of a linear equation with one independent variable is a _____.

Rental-Car Costs. During one month, the Avis Rent Car rate for renting a Buick LeSabre in Mobile, Alabama, was $68.22$per day plus $0.25$per mile. For a one day rental, let $x$denote the number of miles driven and let $y$denote the total cost, in dollars.. The linear equation is $y=68.22+0.25x$

a. Find the y-intercept and slope of the specified linear equation.
b. Explain what the y-intercept and slope represent in terms of the graph of the equation.
c. Explain what the y-intercept and slope represent in terms relating to the application.

Road Grade. The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with a positive grade, $g$. Suppose that you begin driving on that road at an altitude $a_0$

a. Find the linear equation that expresses the altitude, $a$, when you have driven a distance, $d$,along the road. (Hint: Draw a graph and apply the Pythagorean Theorem

b. Identify and interpret the $y$-intercept and slope of the linear equation in part (a).

c. Apply your results in parts (a) and (b) to a road with a $5\%$grade and an initial altitude of $1mile$. Express your answer for the slope to four decimal places.

d. For the road in part (c). what altitude will you reach after driving $10miles$along the road?

e. For the road in part (c), how far along the road must you drive to reach an altitude of $3miles$?

Fill in the blanks.

a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.

b. In regression analysis, an_______ is a data point where removal causes the regression equation to change considerably:

For which of the following sets of data points can you reasonably determine a regression line? Explain your answer.

(a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables for $x,y,e,e^2,\hat{y}$

(c) Determine which line fits the data points better according to the least-square criterion.