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Chapter 4: Q.4.15 (page 190)

Height and Score. A random sample of 10students was taken from an introductory statistics class. The following data were obtained, where Xdenotes height, in inches, and Ydenotes score on the final exam.

a. What sort of value of rwould you expect to find for these data? Explain your answer.

b. Compute r.

Short Answer

Expert verified

(a) The expected value of ris about 0

(b) r=0.0872

Step by step solution

01

Part (a) Step 1: Given information

Given table is

We have to explain the expected value ofr

02

Part (a) Step 2: Explanation

About 0since, in general, it is impossible to establish if the shortest student in a class of students scores worse or higher than the other students. As a result, ifX decreases, Y cannot drop or rise.

03

Part(b) Step1: Given Information

The given table is

We have to computer

04

Part (b) Step 2: Explanation

The formula of linear correlation coefficient is

r=鈭�xiyi-鈭�xi鈭�yi/n鈭�xi2-鈭�xi2/n鈭�yi2-鈭�yi2/n

As shown in the table below, the appropriate value can be determined.

therefore,

r=49596-(668)(742)/1044700-(668)2/1056622-(742)2/10=0.0872

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Most popular questions from this chapter

Shortleaf Pines. The data from Exercise 4.80 for volume, in cubic feet, and diameter at breast height, in inches, for 70shortleaf pines are on the WeissStats site.

  1. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b)and (c).
  2. obtain the linear correlation coefficient
  3. interpret the value of rin terms of the linear relationship between the two variables in question.

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

Acreage and Value. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the Weiss Stats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

a. Obtain a scatterplot for the data.

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

In Exercise 4.11, we give linear equations. For each equation,

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

y=2

In Exercise 4.10, we give linear equations. For each equation,

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

y=-0.75x-5
See all solutions

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