Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 4.2, Problem 3E
Roll a fair four-sided die twice. Let X equal the outcome of the first roll, and let Y equal the sum of the two rolls.
(a) Determine
(b) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
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Solve b
At a large state university, the Statistics department is interested in tracking the progress of its students from entry until graduation. In this example:
X represents a student’s final numeric grade (out of 100) in an introductory statistics course
Y represents a student’s final numeric grade (out of 100) in an upper-level statistics course
The least-squares regression equation for this relationship is: Y = 5.70 + 0.91X
What is the slope of the regression line? Provide a numeric value as shown in the equation.
The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is
y=1.482x−78.952.
Average Weekly Wages (state), x Average Weekly Wages (federal), y754 994762 1037797 1106802 1151844 1201884 1260934 1270945 1310
(a) Find the coefficient of determination and interpret the result.
r2=
(Round to three decimal places as needed.)
Complete parts (a) and (b) below.
(b) Find the standard error of estimate
se and interpret the result.
Se=
(Round to three decimal places as needed.)
Chapter 4 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 4.1 - For each of the following functions, determine the...Ch. 4.1 - Roll a pair of four-sided dice, one red and one...Ch. 4.1 - Let the joint pmf of X and Y be defined by...Ch. 4.1 - Select an (even) integer randomly from the set...Ch. 4.1 - Each part of Figure 4.1-5 depicts the sample space...Ch. 4.1 - The torque required to remove bolts in a steel...Ch. 4.1 - A particle starts at (0,0) and moves in one-unit...Ch. 4.1 - In a smoking survey among boys between the ages of...Ch. 4.1 - A manufactured item is classified as good, a...Ch. 4.2 - Prob. 1E
Ch. 4.2 - Prob. 2ECh. 4.2 - Roll a fair four-sided die twice. Let X equal the...Ch. 4.2 - Let X and Y have a trinomial distribution with...Ch. 4.2 - Prob. 5ECh. 4.2 - The joint pmf of X and Y is f(x,y)=16,0x+y2, where...Ch. 4.2 - Let the joint pmf of X and Y be...Ch. 4.2 - A certain raw material is classified as to...Ch. 4.2 - Prob. 9ECh. 4.2 - If the correlation coefficient exists, show that...Ch. 4.3 - Let X and Y have the joint pmf...Ch. 4.3 - Let the joint pmf f(x,y) of X and Y be given by...Ch. 4.3 - Let W equal the weight of laundry soap in a...Ch. 4.3 - The gene for eye color in a certain male fruit fly...Ch. 4.3 - Let X and Y have a trinomial distribution with...Ch. 4.3 - An insurance company sells both homeowners...Ch. 4.3 - Using the joint pmf from Exercise 4.2-3, find the...Ch. 4.3 - A fair six-sided die is rolled 30 independent...Ch. 4.3 - Let X and Y have a uniform distribution on the set...Ch. 4.3 - Let fX(x)=110,x=0,1,2,...,9, and...Ch. 4.3 - Suppose that X has a geometric distribution with...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Show that the expression in the exponent of...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal...Ch. 4.5 - Let X denote the height in centimeters and Y the...Ch. 4.5 - For a freshman taking introductory statistics and...Ch. 4.5 - For a pair of gallinules, let X equal the weight...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal distribution....Ch. 4.5 - In a college health fitness program, let X denote...Ch. 4.5 - For a female freshman in a health fitness program,...Ch. 4.5 - Prob. 12ECh. 4.5 - An obstetrician does ultrasound examinations on...
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