Statistics for Management and Economics
Statistics for Management and Economics
10th Edition
ISBN: 9781285425450
Author: Gerald Keller
Publisher: Cengage Learning
Question
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Chapter 16.4, Problem 23E

(a)

To determine

Draw the scatter diagram.

(a)

Expert Solution
Check Mark

Explanation of Solution

Figure 1 shows the scatter diagram of Y and X.

Statistics for Management and Economics, Chapter 16.4, Problem 23E

In the above figure, the position of the scatters shows a positive relationship between variables Y and X.

Economics Concept Introduction

Scatter diagram: The scatter diagram shows the value of two variables plotted along two axes. Each scatter represents the relationship between the variables.

(b)

To determine

Calculate the linear relationship.

(b)

Expert Solution
Check Mark

Explanation of Solution

The least squares regression line is shown below:

y=b0+b1x

Where b0 is the y-intercept and b1 is the slope of the regression line.

The least squares regression line is calculated as follows:

Table 1

 XiYiXi2Yi2XiY1
1325962575
251102512100550
32948118
4625036625001500
513193
6471165041284
Total214689180,3562,430

These table values are obtained using a spreadsheet.

i=1nxi=21,i=1nyi=486i=1nxi2=91,i=1nyi2=80,356i=1nxiyi=2,430sxy=1n1[i=1nxiyii=1nxii=1nyin]=161[2,430(21)(468)6]=158.4sx2=1n1[i=1nxi2(i=1nxi)2n]=161[91(21)26]=3.50sy2=1n1[i=1nyi2(i=1nyi)2n]=161[80,356(468)26]=8,770b1=sxysx2 =158.43.5=45.26SSE=(n1)(sy2sxy2sx2)=(61)(8,770(158.4)23.50)=8,006sε=SSEn2=8,00262=844.74H0:β1=0, H1:β1¹0sb1=sε(n1)sx2=44.74(61)(3.50)=10.69t=b1β1sb1=45.26010.69=4.23

This calculation is enough evidence to conclude that variables X and Y are in a linear relationship.

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Chapter 16 Solutions

Statistics for Management and Economics

Ch. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Prob. 20ECh. 16.3 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Prob. 25ECh. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Prob. 33ECh. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Prob. 43ECh. 16.4 - Prob. 44ECh. 16.4 - Prob. 45ECh. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.4 - Prob. 49ECh. 16.4 - Prob. 50ECh. 16.4 - Prob. 51ECh. 16.4 - Prob. 52ECh. 16.4 - Prob. 53ECh. 16.4 - Prob. 54ECh. 16.4 - Prob. 55ECh. 16.4 - Prob. 56ECh. 16.4 - Prob. 57ECh. 16.4 - Prob. 58ECh. 16.4 - Prob. 59ECh. 16.4 - Prob. 60ECh. 16.4 - Prob. 61ECh. 16.4 - Prob. 62ECh. 16.4 - Prob. 63ECh. 16.4 - Prob. 64ECh. 16.4 - Prob. 65ECh. 16.5 - Prob. 66ECh. 16.5 - Prob. 67ECh. 16.5 - Prob. 68ECh. 16.5 - Prob. 69ECh. 16.5 - Prob. 70ECh. 16.5 - Prob. 71ECh. 16.5 - Prob. 72ECh. 16.5 - Prob. 73ECh. 16.5 - Prob. 74ECh. 16.5 - Prob. 75ECh. 16.5 - Prob. 76ECh. 16.5 - Prob. 77ECh. 16.5 - Prob. 78ECh. 16.5 - Prob. 79ECh. 16.5 - Prob. 80ECh. 16.5 - Prob. 81ECh. 16.5 - Prob. 82ECh. 16.5 - Prob. 83ECh. 16.5 - Prob. 84ECh. 16.5 - Prob. 85ECh. 16.5 - Prob. 86ECh. 16.5 - Prob. 87ECh. 16.5 - Prob. 88ECh. 16.5 - Prob. 89ECh. 16.5 - Prob. 90ECh. 16.5 - Prob. 91ECh. 16.5 - Prob. 92ECh. 16.5 - Prob. 93ECh. 16.5 - Prob. 94ECh. 16.5 - Prob. 95ECh. 16.5 - Prob. 96ECh. 16.5 - Prob. 97ECh. 16.5 - Prob. 98ECh. 16.5 - Prob. 99ECh. 16.5 - Prob. 100ECh. 16.6 - Prob. 101ECh. 16.6 - Prob. 102ECh. 16.6 - Prob. 103ECh. 16.6 - Prob. 104ECh. 16.6 - Prob. 105ECh. 16.6 - Prob. 106ECh. 16.6 - Prob. 107ECh. 16.6 - Prob. 108ECh. 16.6 - Prob. 109ECh. 16.6 - Prob. 110ECh. 16.6 - Prob. 111ECh. 16.6 - Prob. 112ECh. 16.6 - Prob. 113ECh. 16.6 - Prob. 114ECh. 16.6 - Prob. 115ECh. 16.6 - Prob. 116ECh. 16.6 - Prob. 117ECh. 16.6 - Prob. 118ECh. 16.A - Prob. 1ECh. 16.A - Prob. 2ECh. 16.A - Prob. 3ECh. 16.A - Prob. 4ECh. 16.A - Prob. 5ECh. 16.A - Prob. 6ECh. 16.A - Prob. 7ECh. 16.A - Prob. 8ECh. 16.A - Prob. 9ECh. 16.A - Prob. 10ECh. 16.A - Prob. 11ECh. 16.A - Prob. 12ECh. 16.A - Prob. 13ECh. 16.A - Prob. 14ECh. 16.A - Prob. 15ECh. 16.A - Prob. 16ECh. 16 - Prob. 119CECh. 16 - Prob. 120CECh. 16 - Prob. 121CECh. 16 - Prob. 122CECh. 16 - Prob. 123CECh. 16 - Prob. 124CECh. 16 - Prob. 125CECh. 16 - Prob. 126CECh. 16 - Prob. 127CECh. 16 - Prob. 128CECh. 16 - Prob. 129CE
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