Statistics for Management and Economics (Book Only)
Statistics for Management and Economics (Book Only)
11th Edition
ISBN: 9781337296946
Author: Gerald Keller
Publisher: Cengage Learning
Question
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Chapter 4.4, Problem 86E

(a)

To determine

Determine the covariance.

(a)

Expert Solution
Check Mark

Explanation of Solution

Covariance is a measure that is used to measure the relationship between the movements of two variables. Thus, covariance measures how changes in one variable are associated with the changes in a second variable. Therefore, covariance measures the degree to which two variables are linearly associated. In this case, covariance can be measured after calculating the square of x and y and the product of xy as follows:

xiyixi2yi2xiyi
4077160059293080
4263176439692646
3779136962412923
4786220973964041
255162526011276
4478193660843432
4183168168893403
4890230481004320
3565122542252275
284774822091316
i=1nxi=387i=1nyi=719i=1nxi2=15,497i=1nyi2=53,643i=1nxiyi=28,712

Covariance can be calculated as follows:

sxy=1n1[i=1nxiyii=1nxii=1nyin]=1101[28,712(387)(719)10]=98.52

The values of two standard deviations can be calculated as follows:

sx2=1n1[i=1nxi2(i=1nxi)2n]=1101[15,497(387)210]=57.79

sy2=1n1[i=1nyi2(i=1nyi)2n]=1101[53,643(719)210]=216.32

Economics Concept Introduction

Covariance: Covariance is a measure that is used to measure the relationship between the movements of two variables.

(b)

To determine

Determine the coefficient of correlation.

(b)

Expert Solution
Check Mark

Explanation of Solution

The coefficient of correlation can be calculated by dividing the covariance with the product of the two sample deviations as follows:

Coefficient of correlation=CovariancexyStandard deviationxStandard deviationy=SxySxSy=98.52(57.79)(216.32)=0.8811

Thus, the coefficient of correlation is calculated to be 0.8811.

(c)

To determine

Determine the coefficient of determination.

(c)

Expert Solution
Check Mark

Explanation of Solution

The coefficient of determination can be calculated by squaring the coefficient of correlation as follows:

Coefficient of determination=(Coefficient of correlation)2=(0.8811)2=0.7763

Thus, the coefficient of determination is calculated to be 0.7763.

(d)

To determine

Determine the least squares line.

(d)

Expert Solution
Check Mark

Explanation of Solution

The covariance is calculated to be 98.52 and the value of S2x is 57.79. Thus, the value of b1 can be calculated as follows:

b1=SxyS2x=98.5257.79=1.705

The values of X¯ and Y¯ can be calculated as follows:

X¯=Xin=38710=38.7

Similarly,

Y¯=Yin=71910=71.9

The value of b0 can be calculated as follows:

b0=Y¯b1X¯=71.9(1.705×38.7)=5.917

The least square line will thus be y^=5.917+1.705x.

(e)

To determine

Determine the indication of the least square line.

(e)

Expert Solution
Check Mark

Explanation of Solution

The results show that there is a very strong positive linear relationship that exists between the two variables taken to analysis. This means that there is a strong positive linear relationship between the time taken to study and the marks obtained. Each additional hour for the study leads to an increase in the marks, and it is on an average by 1.705.

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Chapter 4 Solutions

Statistics for Management and Economics (Book Only)

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Xr04-105 The number of wins, team payrolls, home...Ch. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.5 - Prob. 111ECh. 4.5 - Prob. 112ECh. 4.5 - Prob. 113ECh. 4.5 - Prob. 114ECh. 4.5 - Prob. 115ECh. 4.5 - Prob. 116ECh. 4.5 - Prob. 117ECh. 4.5 - Prob. 118ECh. 4.5 - Prob. 119ECh. 4.5 - Prob. 120ECh. 4.5 - Prob. 121ECh. 4.5 - Prob. 122ECh. 4.5 - Prob. 123ECh. 4.5 - Prob. 124ECh. 4.5 - Prob. 125ECh. 4.5 - Prob. 126ECh. 4.5 - Prob. 127ECh. 4.5 - Prob. 128ECh. 4.5 - Prob. 129ECh. 4.5 - Prob. 130ECh. 4.5 - Prob. 131ECh. 4.6 - Prob. 132ECh. 4.6 - Prob. 133ECh. 4.6 - Prob. 134ECh. 4.6 - Prob. 135ECh. 4.6 - Prob. 136ECh. 4.6 - Prob. 137ECh. 4.6 - Prob. 138ECh. 4 - Prob. 139CECh. 4 - Prob. 140CECh. 4 - Prob. 141CECh. 4 - Prob. 142CECh. 4 - Prob. 143CECh. 4 - Prob. 144CECh. 4 - Prob. 145CECh. 4 - Prob. 146CECh. 4 - Prob. 147CECh. 4 - Prob. 148CECh. 4 - Prob. 149CECh. 4 - Prob. 150CECh. 4 - Prob. 151CECh. 4 - Prob. 152CECh. 4 - Prob. 153CECh. 4 - Prob. 154CE
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